rate distortion optimal fast thresholding with complete jpeg mpeg decoder compatibility we show a rate distortion optimal way to threshold or drop the dct coefficients of the jpeg and mpeg compression standards our optimal algorithm uses a fast dynamic programming recursive structure the primary advantage of our approach lies in its complete compatibility with standard jpeg and mpeg decoders

new good quasi cyclic ternary and quaternary linear codes let n k d q codes be linear codes of length n dimension k and minimum hamming distance d over gf q the following quasi cyclic codes are constructed in this paper 44 11 20 3 55 11 26 3 66 11 32 3 48 12 21 3 60 12 28 3 56 13 24 3 65 13 29 3 56 14 23 3 60 15 23 3 64 16 25 3 36 9 19 4 90 9 55 4 99 9 61 4 30 10 14 4 50 10 27 4 55 10 30 4 33 11 15 4 44 11 22 4 55 11 29 4 36 12 16 4 48 12 23 4 60 12 31 4 all of these codes have established or exceed the respective lower bounds on the minimum distance given by brouwer

fisher information and stochastic complexity by taking into account the fisher information and removing an inherent redundancy in earlier two part codes a sharper code length as the stochastic complexity and the associated universal process are derived for a class of parametric processes the main condition required is that the maximum likelihood estimates satisfy the central limit theorem the same code length is also obtained from the so called maximum likelihood code

the effect of network topology on the stability of discrete state models of genetic control boolean networks have been proposed as potentially useful models for genetic control an important aspect of these networks is the stability of their dynamics in response to small perturbations previous approaches to stability have assumed uncorrelated random network structure real gene networks typically have nontrivial topology significantly different from the random network paradigm to address such situations we present a general method for determining the stability of large boolean networks of any specified network topology and predicting their steady state behavior in response to small perturbations additionally we generalize to the case where individual genes have a distribution of expression biases and we consider a nonsynchronous update as well as extension of our method to non boolean models in which there are more than two possible gene states we find that stability is governed by the maximum eigenvalue of a modified adjacency matrix and we test this result by comparison with numerical simulations we also discuss the possible application of our work to experimentally inferred gene networks

on k t subnormal covering codes the concept of a k t subnormal covering code is defined it is discussed how an amalgamated direct sumlike construction can be used to combine such codes the existence of optimal q n m 1 codes c is discussed such that by puncturing the first coordinate of c one obtains a code with q 1 subnorm 2

a note on bounds for q ary covering codes two strongly seminormal codes over z sub 5 are constructed to prove a conjecture of ostergard see ibid vol 37 no 3 p 660 4 1991 it is shown that a result of honkala see ibid vol 37 no 4 p 1203 6 1991 on k t subnormal codes holds also under weaker assumptions a lower bound and an upper bound on k sub q n r the minimal cardinality of a q ary code of length n with covering radius r are obtained these give improvements in seven upper bounds and twelve lower bounds by ostergard for k sub q n r for q 3 4 and 5

linear codes with covering radius 2 and other new covering codes infinite families of linear binary codes with covering radius r 2 and minimum distance d 3 and d 4 are given using the constructed codes with d 3 r 2 families of covering codes with r 2 are obtained the parameters of many constructed codes with r

low dimensional lattices ii subgroups of gl n ℤ the maximal finite irreducible groups of n x n integers for n 4 5 9 11 13 17 19 23 were determined by dade ryskov bulow plesken pohst and plesken as the automorphism groups of certain quadratic forms this paper presents a geometric description of the corresponding n dimensional lattices and gives coordinates which display their symmetries and minimal vectors some very interesting lattices appear

an improvement of the van wee bound for binary linear covering codes the van wee bound gives a lower bound on the cardinality of block codes with a prescribed covering radius the author presents an improvement of this bound for binary linear codes and compares the results with other bounds mentioned in the literature almost all reported bounds can be obtained via the present bound as well moreover the present authors obtain a number of new lower bounds

lower bounds for binary codes of covering radius one let k n l denote the minimal cardinality of a binary code of length n and covering radius one blass and litsyn proved a lower bound k n l for in the case n equiv 5 mod6 we give a simplification of the proof which yields a slightly better result

modified bounds for covering codes the covering radius of binary codes is studied bounds on k n r the minimum cardinality of any binary code of length n and covering radius r are found modifications of the van wee lower bounds are proved for k n r the minimal number of codewords in any binary code of length n and covering radius r the first of the two van wee bounds is based on studying the hamming spheres of radius 1 centered at the points which have distance r to the code c the points covered by more than one codeword are divided into several classes and better estimates for some of these classes are obtained using a suitable averaging process the lower bound for k n r when r or 2 is improved the second van wee bound studies spheres of radius 2 centered at the points which have distance r 1 or r to the code c these points are divided essentially into two classes the points that are covered by only one codeword of c and the points that are covered by more than one codeword

further results on k t subnormal covering codes the concept of k t subnormal covering codes is discussed generalizing some of the earlier results in a similar way k t normal covering codes are defined using the results including some new constructions upper bounds for covering codes are improved it is shown how simulated annealing can be used to find acceptable partitions for codes

the covering radius of the 2 15 16 reed muller code is at least 16276 two interesting cosets of the first order reed muller code of block length 2 15 are described they provide counterexamples to a conjecture on the covering radius

on the structure of linear codes with covering radius two and three we obtain new bounds on l m r the minimum length of a linear code with codimension m and covering radius r all bounds are derived in a uniform way we employ results from coding theory some earlier results on covering codes and combinatorial arguments we prove the following bounds l 6 2 13 l 7 2 19 l 8 2 spl ges 25 l 9 2 spl ges 34 l 2m l 2 spl ges 2 sup m 1 for m spl ges 3 l 14 2 spl ges 182 l 16 2 spl ges 363 l 18 2 spl ges 725 l 20 2 spl ges 1449 l 22 2 spl ges 2897 l 24 2 spl ges 5794 l 9 3 spl ges 17 l 10 3 spl ges 21 l 12 3 spl ges 31 l 13 3 spl ges 38

reduced complexity delayed decision algorithm for context based image processing systems it is well known that the performance of context based image processing systems can be improved by allowing the processor e g an encoder or a denoiser a delay of several samples before making a processing decision often however for such systems traditional delayed decision algorithms can become computationally prohibitive due to the growth in the size of the space of possible solutions in this paper we propose a reduced complexity one pass delayed decision algorithm that systematically reduces the size of the search space while also preserving its structure in particular we apply the proposed algorithm to two examples of adaptive context based image processing systems an image coding system that employs a context based entropy coder and a spatially adaptive image denoising system for these two types of widely used systems we show that the proposed delayed decision search algorithm outperforms instantaneous decision algorithms with only a small increase in complexity we also show that the performance of the proposed algorithm is better than that of other higher complexity delayed decision algorithms

lossy cutset coding of bilevel images based on markov random fields an effective low complexity method for lossy compression of scenic bilevel images called lossy cutset coding is proposed based on a markov random field model it operates by losslessly encoding pixels in a square grid of lines which is a cutset with respect to a markov random field model and preserves key structural information such as borders between black and white regions relying on the markov random field model the decoder takes a map approach to reconstructing the interior of each grid block from the pixels on its boundary thereby creating a piecewise smooth image that is consistent with the encoded grid pixels the map rule which reduces to finding the block interiors with fewest black white transitions is directly implementable for the most commonly occurring block boundaries thereby avoiding the need for brute force or iterative solutions experimental results demonstrate that the new method is computationally simple outperforms the current lossy compression technique most suited to scenic bilevel images and provides substantially lower rates than lossless techniques e g jbig with little loss in perceived image quality

lossless near lossless and refinement coding of bilevel images we present general and unified algorithms for lossy lossless coding of bilevel images the compression is realized by applying arithmetic coding to conditional probabilities as in the current jbig standard the conditioning may be specified by a template for better compression the more general free tree may be used loss may be introduced in a preprocess on the encoding side to increase compression the primary algorithm is a rate distortion controlled greedy flipping of pixels though being general the algorithms are primarily aimed at material containing half toned images as a supplement to the specialized soft pattern matching techniques that work better for text template based refinement coding is applied for lossy to lossless refinement introducing only a small amount of loss in half toned test images compression is increased by up to a factor of four compared with jbig lossy lossless and refinement decoding speed and lossless encoding speed are less than a factor of two slower than jbig the de coding method is proposed as part of jbig2 an emerging international standard for lossless lossy compression of bilevel images

on the covering radius of codes the covering radius r of a code is the maximal distance of any vector from the code this work gives a number of new results concerning t n k the minimal covering radius of any binary code of length n and dimension k for example t n 4 and t n 5 are determined exactly and reasonably tight bounds on t n k are obtained for any k when n is large these results are found by using several new constructions for codes with small covering radius one construction the amalgamated direct sum involves a quantity called the norm of a code codes with norm leq 2 r 1 are called normal and may be combined efficiently the paper concludes with a table giving bounds on t n k for n leq 64

computing automorphism groups of error correcting codes an algorithm is described for computing the automorphism group of an error correcting code the algorithm determines the order of the automorphism group and produces a set of monomial permutations which generate the group it has been implemented on a computer and has been used successfully on a great number of codes of moderate length

constructions families and tables of binary linear covering codes presents constructions and infinite families of binary linear covering codes with covering radii r 2 3 4 using these codes the authors obtain a table of constructive upper bounds on the length function l r r for r spl les 64 and r 2 3 4 where l r r is the smallest length of a binary linear code with given codimension r and covering radius r they obtain also upper bounds on l r r for r 21 28 r 5 parameters of the constructed codes are better than parameters of previously known codes

constructions of nonlinear covering codes constructions of nonlinear covering codes are given using any nonlinear starting code of covering radius r spl ges 2 these constructions form an infinite family of codes with the same covering radius a nonlinear code is treated as a union of cosets of a linear code new infinite families of nonlinear covering codes are obtained concepts of r l objects r l partitions and r l length are described for nonlinear codes

new lower bounds for binary covering codes g d chen et al ibid vol it 32 p 680 94 1986 presented two new lower bounds for k n r where k n r denotes the minimum cardinality of a binary code of length n and covering radius r the author shows that a slight modification gives further improvements and some examples are given to confirm the argument codes that have a certain partitioning property are considered

on the covering radius of binary 14 6 codes containing the all one vector it is shown that the covering radius of any binary linear 14 6 code containing the all one vector is at least 4 since the minimum covering radius of a binary linear 14 6 code is 3 this shows that in general the minimum of the covering radius is not achieved by codes containing the all one vector

criticality in random threshold networks annealed approximation and beyond random threshold networks with sparse asymmetric connections show complex dynamical behavior similar to random boolean networks with a transition from ordered to chaotic dynamics at a critical average connectivity kc in this type of model contrary to boolean networks propagation of local perturbations damage depends on the in degree of the sites kc is d eterminedanalytically using an annealedapproximation andthe results are con2rmedby numerical simulations it is shown that the statistical distributions of damage spreading near the percolation transition obey power laws andd ynamical correlations between active network clusters become maximal we investigate the e4ect of local damage suppression at highly connected nodes for networks with scale free in degree distributions possible relations of our 2ndings to properties of real world networks like robustness and non trivial degree distributions are discussed c

linear inequalities for covering codes ii triple covering inequalities the lower bounds on k n r minimum number of codewords of any binary code of length n and covering radius r are improved a new technique combining the hamming association scheme and the results of a classic problem of covering pairs by k tuples is introduced the new lower bounds are obtained by studying various linear inequalities satisfied by covering codes and such an inequality is derived the lower bounds for k n r are studied for some special values of n and r which serve as examples showing how the methods developed are applied to concrete cases

subcodes and covering radius corresp a sharp lower bound on the covering radius of a linear binary code is given in terms of the covering radius of any subcode of index two an upper bound on the norm of a code is then derived these results hold for all linear codes over gf 2

a sequence based extension of mean field annealing using the forward backward algorithm application to image segmentation optimization based on mean field theory including mean field annealing mfa is widely used for discrete optimization label assignment problems defined on the pixel sites of an image one formulation of mfa is via maximum entropy where one seeks the joint distribution over the random assignments subject to an average level of cost mfa is obtained by assuming the assignments at each pixel are statistically independent given the observed image alternatively we make the less restrictive assumption of independent row labelings the independence assumption means that at each step mfa optimizes over only one pixel whereas our method jointly optimizes over an entire row i e our method is less greedy in principle an mfa extension could be developed that explicitly re estimates the row labeling distributions but such an approach is in practice infeasible even so we can indirectly implement this re estimation by re estimating quantities that determine the row labeling distributions these quantities are the a posteriori site probabilities re estimable via the well known forward backward f b algorithm thus our algorithm which descends in the me lagrangian free energy consists of iterative application of f b to the image rows columns at convergence maximum a posteriori site labeling is performed our method was applied to segmentation of both real and synthetic noise corrupted images it achieved lower markov random field model potentials and better segmentations compared with other methods and in high noise standard mfa

binary linear quasi perfect codes are normal whether quasi perfect codes are normal is addressed let c be a code of length n dimension k covering radius r and minimal distance d it is proved that c is normal if d or 2r 1 hence all quasi perfect codes are normal consequently any n k r binary linear code with minimal distance d or 2r 1 is normal

further results on the covering radius of codes a number of upper and lower bounds are obtained for k n r the minimal number of codewords in any binary code of length n and covering radius r several new constructions are used to derive the upper bounds including an amalgamated direct sum construction for nonlinear codes this construction works best when applied to normal codes and we give some new and stronger conditions which imply that a linear code is normal an upper bound is given for the density of a covering code over any alphabet and it is shown that k n 2 r 1 leq k n r holds for sufficiently large n

more binary covering codes are normal it is shown that every optimal binary code with covering radius r 1 is normal this parity proves a conjecture of cohen lobstein and sloane 1986 it is also proved that codes with minimal distance 2r or 2r 1 are normal a generalization of frankl s construction 1987 of abnormal codes is given

several new lower bounds on the size of codes with covering radius one we derive several new lower bounds on the size of binary codes with covering radius one in particular we prove k

on the hardness of decoding the gale berlekamp code the gale berlekamp in short gb code is the dual code of the binary product code in which the horizontal and vertical constituent codes are both the parity code it is shown that the problem of deciding whether there is a codeword of the gb code within a prescribed distance from a given received word is np complete the problem remains hard in a well defined sense even if the decoder is allowed unlimited preprocessing that depends only on the code length while the intractability of maximum likelihood decoding mld for specific codes has already been shown by bruck and naor lobstein and guruswami and vardy the result herein seems to be the first that shows hardness for a natural code in particular without any tailoring of the definition or the parameters of the code to suit the hardness proof in contrast it is also shown that with respect to any memoryless binary symmetric channel bsc with crossover probability less than 1 2 mld can be implemented in linear time for all error events except for a portion that occurs with vanishing probability

improved sphere bounds on the covering radius of codes the sphere bound is a trivial lower bound on k n r the minimal cardinality of any binary code of length n and with covering radius r by simple arguments it is considerably improved to k n 1 or 2 sup n n for n even a table of lower and upper bounds on k n r for n

upper bounds for q ary covering codes new methods for constructing q ary covering codes are presented the author introduces the concepts of p seminormal and strongly p seminormal codes and shows how seminormal codes and punctured hamming codes can be combined to construct new covering codes using these methods upper bounds for ternary covering codes are improved the new bounds are k sub 3

some results on the norm of codes two upper bounds for the norm n c of a binary linear code c with minimal weight d and covering radius r are given the second of these bounds implies that c is normal if r 3

a 55 16 19 binary goppa code and related codes having large minimum distance a 55 16 19 binary goppa code is used to construct 57 17 17 58 17 18 59 17 19 and 60 17 20 codes the first two codes have smaller redundancy than previously known codes linear or nonlinear of the same length and minimum distance the last two codes have parameters previously attained only by nonlinear codes

lower bounds on t n k from linear inequalities the linear inequality method for covering codes is used to improve the lower bounds of t n k the smallest covering radius of any n k binary linear code to make better use of the strength of this method the relation between the covering radius of a code and the minimum distance of its dual code is studied the authors obtained 65 improved lower bounds for t n k within the range of n

on binary linear codes which satisfy the two way chain condition general constructions of binary linear codes satisfying the two way chain condition are found sufficient conditions for their existence are determined some of these codes are proven to be z sub 4 linear an expression for their state complexity profile is also found cases when such codes have covering radius r t n k are shown

the covering radius of cyclic codes of length up to 31 corresp the covering radius is given for all binary cyclic codes of length less than or equal to 31 many of these codes are optimal in the sense of having the smallest possible covering radius of any linear code of that length and dimension

inequalities for covering codes any code c with covering radius r must satisfy a set of linear inequalities that involve the lloyd polynomial l sub r x these generalize the sphere bound syndrome graphs associated with a linear code c are introduced to help keep track of low weight vectors in the same coset of c if there are too many such vectors c cannot exist illustrations show that t 17 10 3 and t 23 15 3 where t n k is the smallest covering radius of any n k code

do most binary linear codes achieve the goblick bound on the covering radius corresp the following two problems are dealt with p1 finding the smallest rate r of a binary code of length n admitting a prescribed covering radius rho n p2 discovering whether a majority of codes with any rate larger than r admits the given covering radius for the class of unrestricted nonlinear codes a solution to both problems is obtained by an elementary averaging argument the solution to p1 is r 1 h rho o n 1 log n and the answer to p2 is positive as for the more interesting class of linear codes goblick s extension method shows that the solution to p1 is the same as in the unrestricted case in contrast p2 seems to remain an open question a simple derivation of goblick s result is presented and a discussion is made of the positive conjecture concerning p2 for linear codes

new covering codes from an ads like construction a covering code construction is presented using this construction it is shown that t 52 39 3 t 36 21 4 t 58 32 7 k 32 2 spl les 62 spl middot 2 sup 18 and k 62 5 spl les 31 spl middot 2 sup 37 where t n k is the minimum covering radius among all binary n k codes and k n r is the minimum cardinality of a binary code of length n and covering radius r four new linear codes found by computer search are also given these include a 23 9 5 code a 32 8 10 code a 51 41 2 code and a 45 20 8 code

binary and ternary linear quasi perfect codes with small dimensions the aim of this work is a systematic investigation of the possible parameters of quasi perfect qp binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes first we give a list of infinite families of qp codes which includes all binary ternary and quaternary codes known to us we continue further with a list of sporadic examples of binary and ternary qp codes later we present the results of our investigation where binary qp codes of dimensions up to 14 and ternary qp codes of dimensions up to 13 are classified

packing and covering properties of rank metric codes this paper investigates packing and covering properties of codes with the rank metric first we investigate packing properties of rank metric codes then we study sphere covering properties of rank metric codes derive bounds on their parameters and investigate their asymptotic covering properties

frequency computation and bounded queries there have been several papers over the last ten years that consider the number of queries needed to compute a function as a measure of its complexity the following function has been studied extensively in that light faa x1 xa a x1 a xa we are interested in the complexity in terms of the number of queries of approximating faa let b a and let f be any function such that faa x1 xa and f x1 xa agree on at least b bits for a general set a we have matching upper and lower bounds on f that depend on coding theory these are applied to get exact bounds for the case where a is semirecursive a is superterse and assuming p np a sat we obtain exact bounds when a is the halting problem using different methods

constructions for perfect mixed codes and other covering codes a construction for an infinite family of perfect mixed codes with covering radius 2 is presented these are the first known nontrivial perfect mixed codes with covering radius greater than 1 based on mixed codes constructions for binary covering codes that lead to a considerable improvement of upper bounds on the sizes of covering codes are presented these codes and some other codes can be obtained by the blockwise direct sum construction two infinite families of codes are of special interest they are quasi perfect nonlinear union of their disjoint translates covers the space and their density as covering codes is remarkably low

on the string consensus problem and the manhattan sequence consensus problem abstract we study the manhattan sequence consensus problem msc problem in which we are given k integer sequences each of length l and we are to find an integer sequence x of length l called a consensus sequence such that the maximum manhattan distance of x from each of the input sequences is minimized a related problem with hamming distance instead of manhattan distance is called hamming string consensus hsc also known under the names of string center problem or closest string problem for binary sequences manhattan distance coincides with hamming distance hence in this case hsc is a special case of msc we design a practically efficient o l time algorithm solving msc for k 5 sequences it improves upon the quadratic algorithm by amir et al 2012 1 for hsc for k 5 binary strings similarly as in the algorithm of amir et al we use a column based framework we replace the implied general integer linear programming by its easy special cases due to combinatorial properties of msc for k 5 practicality of our algorithms has been verified experimentally we also show that for a general parameter k any instance can be reduced in linear time to a kernel of size k so the problem is fixed parameter tractable nevertheless for k 4 this is still too large for any naive solution to be feasible in practice this is a full version of an article published at spire 2014 15

new binary covering codes obtained by simulated annealing new binary covering codes of radius 1 obtained by simulated annealing are presented these constructions establish that k 9 1 spl les 62 and k 12 1 spl les 380 the article is concerned with finding upper bounds on k n r the minimum cardinality of any binary code of length n and with covering radius r

some new lower bounds for binary and ternary covering codes a modified lower bound for binary codes with covering radius one is derived let k sub q n r denote the minimum cardinality of a q ary code with covering radius r the new bound shows that k sub 2 11 1 or 177 and that k sub 2 17 1 or 7391 improvements of the best lower bounds known the authors also generalize a known lower bound for binary codes to the case of arbitrary q for q 3 this simple bound improves the best lower bounds known in several cases an updated version of a table for k sub 3 n r is included

new lower bounds for covering codes some new lower bounds on mod c mod for a binary linear n k r code c with n 1 t r 1 r 0 2 odd or with n 1 t r 1 1 t 2 even are obtained these bounds improve the sphere covering bound considerably and give several new values and lower bounds for the function t n k the smallest covering radius of any n k code

the multicovering radii of codes the covering radius of a code is the least r such that the set of balls of radius r around codewords covers the entire ambient space we introduce a generalization of the notion of covering radius the m covering radius of a code is the least radius such that the set of balls of that radius covers all m tuples of elements in the ambient space we investigate basic properties of m covering radii we investigate whether codes exist with given m covering radii not always we derive bounds on the size of the smallest code with a given m covering radius based on generalizations of the sphere bound and the method of counting excesses

phase transitions in random networks simple analytic determination of critical points the standard method for determining the critical points in random networks such as boolean nets is based on the derrida approximation this method leads to the critical points based on the so called annealed approximation in this paper we present a very simple annealed approximation based on the study of damage spreading when single elements are modified several examples are analyzed

on the optimal linear receiving filter for digital transmission over nonlinear channels a recent paper by e biglieri et al see ibid vol 35 p 620 5 may 1989 shows that the matched filter tapped delay line structure is optimum not only for linear pulse modulated signals and linear channel distortion but also for nonlinear finite alphabet pulse modulation and some nonlinear channel distortion this has important practical applications therefore its connection with other work reported in the literature is presented

order disorder phase transition in random walk networks in this paper we study in detail the behavior of random walk networks rwn s these networks are a generalization of the well known random boolean networks rbn s a classical approach to the study of the genome rwn s are also discrete networks but their response is defined by small variations in the state of each gene thus being a more realistic representation of the genome and a natural bridge between discrete and continuous models rwn s show a clear transition between order and disorder here we explicitly deduce the formula of the critical line for the annealed model and compute numerically the transition points for quenched and annealed models we show that rbn s and the annealed model of rwn s act as an upper and a lower limit for the quenched model of rwn s finally we calculate the limit of the annealed model for the continuous case

on the norm and covering radius of the first order reed muller codes let spl rho 1 m and n 1 m be the covering radius and norm of the first order reed muller code r 1 m respectively it is known that spl rho 1 2k 1 spl les lower bound 2 sup 2k 2 sup 2k 1 2 and n 1 2k 1 spl les 2 lower bound 2 sup 2k 2 sup 2k 1 2 k 0 we prove that spl rho 1 2k 1 spl les 2 lower bound 2 sup 2k 1 2 sup 2k 3 2 and n 1 2k 1 spl les 4 lower bound 2 sup 2k 1 2 sup 2k 3 2 k 0 we also discuss the connections of the two new bounds with other coding theoretic problems

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

distributed estimation and quantization an algorithm is developed for the design of a nonlinear n sensor distributed estimation system subject to communication and computation constraints the algorithm uses only bivariate probability distributions and yields locally optimal estimators that satisfy the required system constraints it is shown that the algorithm is a generalization of the classical lloyd max results

an improved sphere covering bound for the codes with n 3r 2 let c be a binary code not necessarily linear with covering radius r and length n 3r 2 the sphere covering bound on the cardinality of c is improved considerably provided c has minimal distance d 2 some new results on the function t n k the smallest covering radius of any binary linear code with length n and dimension k t 38 6 or 13 t 47 7 or 16 t 59 8 or 20 are given

explicit codes with low covering radius a series of explicit low rate binary linear codes that have relatively low covering radius and can be rapidly decoded is exhibited these codes can be derived from higher dimensional analogs of the gale berlekamp switching game conjectures of independent interest involving hadamard matrices are given that could yield semiexplicit covering codes of very low density

a new binary code of length 10 and covering radius 1 a mixed code of covering radius 1 that has 60 codewords is constructed this code is then used to show that k 10 1

random walk networks abstract random boolean networks are among the best known systems used to model genetic networks they show an on off dynamics and it is easy to obtain analytical results with them unfortunately very few genes are strictly on off switched on the other hand continuous methods are in principle more suitable to capture the real behavior of the genome but have difficulties when trying to obtain analytical results in this work we introduce a new model of random discrete network random walk networks where the state of each gene is changed by small discrete variations being thus a natural bridge between discrete and continuous models

bounds for abnormal binary codes with covering radius one the normality of binary codes is studied the minimum cardinality of a binary code of length n with covering radius r is denoted by k n r it is assumed that c is an n m r code that is a binary code of length n with m codewords and covering radius r it is shown that if c is an n m 1 code then it is easy to find a normal n m 1 code by changing c in a suitable way and that all the optimal n m 1 codes i e those for which m k n 1 are normal and their every coordinate is acceptable it is shown that if c is an abnormal n m code then n or 9 and an abnormal 9118 1 code which is the smallest abnormal code known at present is constructed lower bounds on the minimum cardinality of a binary abnormal code of length n with covering radius 1 are derived and it is shown that if an n m 1 code is abnormal then m or 96

constructions and families of covering codes and saturated sets of points in projective geometry in davydov 1990 constructions of linear binary covering codes were considered in the present paper constructions and techniques of the earlier paper are developed and modified for q ary linear nonbinary covering codes q spl ges 3 and new constructions are proposed the described constructions design an infinite family of codes with covering radius r based on a starting code of the same covering radius for arbitrary r spl ges 2 q spl ges 3 new infinite families of nonbinary covering codes with good parameters are obtained with the help of an iterative process when constructed codes are the starting codes for the following steps the table of upper bounds on the length function for codes with q 3 r 2 3 and codimension up to 24 is given the author proposes to use saturated sets of points in projective geometries over finite fields as parity check matrices of starting codes new saturated sets are obtained

a universal data compression system a universal data compression algorithm is described which is capable of compressing long strings generated by a finitely generated source with a near optimum per symbol length without prior knowledge of the source this class of sources may be viewed as a generalization of markov sources to random fields moreover the algorithm does not require a working storage much larger than that needed to describe the source generating parameters

cellular automata model for gene networks in order to study the overall behavior of gene networks we propose a simple cellular automata ca model in which each binary gene is connected to k other inputs including itself interacting through asymmetric short and long range couplings using numerical simulations and mean field calculations collective dynamical properties of this ca model were investigated it is shown that the ca exhibits three different dynamical regimes a frozen a marginal and a chaotic phase where an initial damage vanishes remains limited and grows to a finite fraction of the lattice sites respectively the results presented are also consistent with the observed biological scaling laws for the number of differentiated cells and cell length cycles as a function of the number of genes in an organism s1063 651x 97 03303 5

some results on the covering radii of reed muller codes let r r m be the rth order reed muller code of length 2 sup m and let rho r m be its covering radius r

asymptotic bounds on the covering radius of binary codes asymptotic covering properties of families of binary codes are studied a gaussian approximation to the weight distribution of translates for codes of high strength is used from this an upper bound on the covering radius of these codes is deduced applications include reed muller codes quadratic residue codes and bch codes sufficient conditions for a family of codes to have best possible covering radius asymptotically perfect codes are derived

on the covering radius of subcodes of a code let c be a binary linear code with covering radius r and c sub 0 a subcode of c of codimension i an upper bound is obtained for the covering radius of c sub 0 in terms of r and i when c sub 0 0 the bound becomes the sphere covering bound for r

tree coding of bilevel images presently sequential tree coders are the best general purpose bilevel image coders and the best coders of halftoned images the current iso standard joint bilevel image experts group jbig is a good example a sequential tree coder encodes the data by feeding estimates of conditional probabilities to an arithmetic coder the conditional probabilities are estimated from co occurrence statistics of past pixels the statistics are stored in a tree by organizing the code length calculations properly a vast number of possible models trees reflecting different pixel orderings can be investigated within reasonable time prior to generating the code a number of general purpose coders are constructed according to this principle rissanen s 1989 one pass algorithm context is presented in two modified versions the baseline is proven to be a universal coder the faster version which is one order of magnitude slower than jbig obtains excellent and highly robust compression performance a multipass free tree coding scheme produces superior compression results for all test images a multipass free template coding scheme produces significantly better results than jbig for difficult images such as halftones by utilizing randomized subsampling in the template selection the speed becomes acceptable for practical image coding

on normal and subnormal q ary codes the authors extend to the q ary case the notions of a normal code a subnormal code and the amalgamated direct sum construction in order to investigate problems related to the covering radius of codes for example the authors prove that every nonbinary nontrivial perfect code is absubnormal they also include some linear programming lower bounds on ternary codes with covering radius 2 or 3

lower bounds for q ary covering codes the authors prove combinatorial lower bounds for k sub q n r the minimal cardinality of any q ary code of length n and covering radius r tables of lower bounds for k sub q n r are presented for q 3 4 5

a new construction for covering codes a novel method for constructing normal binary nonlinear covering codes is presented the construction improves several upper bounds on k n r the minimum cardinality of a binary code of length n and covering radius r