injectivity of compressing maps on primitive sequences over bbz p e let zopf pe be the integer residue ring with odd prime p and integer eges2 for a sequence a over zopf pe one has a unique p adic expansion a a 0 a 1 p a e 1 pe 1 where a i can be regarded as a sequence over zopf p for 0lesilese 1 let f x be a strongly primitive polynomial over zopf pe and g f x pe be the set of all primitive sequences generated f x by over zopf pe recently the authors xuan yong zhu and wen feng qi have proved that for a function phi x0 xe 1 g xe 1 eta x0 xe 2 over zopf p and a b ising f x pe where 2lesdeg glesp 1 phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b to further complete their work we show that such injectivity also holds for deg g 1 that is for a function phi x0 xe 1 xe 1 eta x0 xe 2 over zopf p and a b ising f x pe phi a 0 a 1 a e 1 phi b 0 b 1 b e 1 if and only if a b

an upper bound on the aperiodic autocorrelation function for a maximal length sequence corresp the magnitude of the out of phase aperiodic autocorrelation function for a maximal length linear feedback shift register sequence of period n is at most 1 2 pi n 1 1 2 ln 4n pi previously the best upper bound was n 1 1 2 ln en

distribution properties of compressing sequences derived from primitive sequences over bbz p e let z pe be the integer residue ring with odd prime p and integer e 2 any sequence a over z pe has a unique p adic expansion a a0 a1 p ae 1 pe 1 where ai can be regarded as a sequence over z p for 0 i e 1 let f x be a strongly primitive polynomial over z pe and a b be two primitive sequences generated by f x over z pe assume x0 xe 1 xe 1 x0 xe 2 is an e variable function over z p with the monomial p 1 2 xe 2 p 1 x1 p 1 not pearing in the expression of x0 x1 xe 2 it is shown that if there exists an s z p such that a0 t ae 1 t s if and only if b0 t be 1 t s for all nonnegative t with i 0 where is an m sequence determined by f x and a0 then a b this implies that for compressing sequences derived from primitive sequences generated by f x over z pe single element distribution is unique on all positions t with t 0 in particular when x0 x1 xe 2 0 it is a completion of the former result on the uniqueness of distribution of element 0 in highest level sequences

product structure of the fuzzy n ary factor polygroup fuzzy n ary hypergroups were introduced as suitable generalizations of fuzzy polygroups and a special case of fuzzy n ary hyper groups the aim of this paper is to introduce the notion of fuzzy n ary factor polygroups of a polygroup based on the fuzzy n ary factor group we also study the product structures of the generating fuzzy factor n ary groups at the end of the paper we prove the fundamental theorem of isomorphism of fuzzy n ary groups

on the distribution of inversive congruential pseudorandom numbers in parts of the period the inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation in this paper we present the first nontrivial bounds on the discrepancy of individual sequences of inversive congruential pseudorandom numbers in parts of the period the proof is based on a new bound for certain incomplete exponential sums

shift register synthesis modulo m the berlekamp algorithm takes a sequence of elements from a field and finds the shortest linear recurrence or linear feedback shift register that can generate the sequence we present an algorithm which generalizes berlekamp s to the case when the elements of the sequence are integers modulo m where m is an arbitrary but known integer details will be published elsewhere

comparison of three correlation coefficient estimators for gaussian stationary processes using independent samples from two stationary gaussian processes second order statistics are examined for the following three correlation estimators 1 the direct estimator 2 a hybrid sign estimator and 3 the polarity coincidence estimator in most cases increasing the number of samples by a factor of two or three allows one to use the simple polarity coincidence estimator with the same accuracy as the other two estimators

strongly transitive geometric spaces associated to hypermodules abstract in this paper we use the strongly regular relation on hypermodules with canonical hypergroup over a given krasner hyperring in this way we consider the fundamental relation defined on a hypermodule and prove some results in this respect also we determine a family p m of subsets of a hypermodule m and we give sufficient conditions such that the geometric space m p m is strongly transitive and the relation is transitive

on the construction of binary sequence families with low correlation and large sizes in this paper we revisit a method to produce binary sequences using the most significant bit map from z4 to the binary field this method is useful for the construction of binary sequences with low correlation and large family size there may be more cases where starting with z4 could help researchers design new low correlation sequences for code division multiple access application

applications of interval valued fuzzy n ary polygroups with respect to t norms t conorms using the triangular norm t conorm s in the context of n ary polygroups we introduce the concept of an interval valued anti fuzzy n ary subpolygroup with respect to t s respectively a necessary and sufficient condition for an interval valued fuzzy subset in order to be an interval valued anti fuzzy n ary subpolygroup is established and some important results are presented this study is useful for the most computational part of fuzzy control which is the defuzzification

on the 2 adic complexity and the k error 2 adic complexity of periodic binary sequences a significant difference between the linear complexity and the 2 adic complexity of periodic binary sequences is pointed out in this correspondence based on this observation we present the concept of the symmetric 2 adic complexity of periodic binary sequences the expected value of the 2 adic complexity is determined and a lower bound on the expected value of the symmetric 2 adic complexity of periodic binary sequences is derived we study the variance of the 2 adic complexity of periodic binary sequences and the exact value for it is given because the k adic complexity of periodic binary sequences is unstable we present the concepts of the kappa error 2 adic complexity and the k error symmetric 2 adic complexity and lower bounds on them are also derived in particular we give tighter upper and lower bounds for the minimum k adic complexity of l sequences by substituting two symbols within one period

a fast digital method of estimating the autocorrelation of a guassian stationary process given a zero mean stationary gaussian process x n it is shown that the autocorrelation can be estimated by hat r xx j c n sum min i 1 max n x i sign x i j where c n frac pi 2n 2 sum min i 1 max n x i this method is attractive since c n needs to he computed only once and sum min i 1 max n x i sign x i j can be computed by additions only moreover the shape of the autocorrelation given by hat r xx j c n can be computed by additions only

design and properties of a new pseudorandom generator based on a filtered fcsr automaton feedback with carry shift registers fcsr was introduced by goresky and klapper in 1993 it is similar to the classical linear feedback shift registers lfsr used in many pseudorandom generators the main difference is that the elementary additions are not additions modulo 2 but with propagation of carries the main problem for the use of an fcsr automaton is the fact that the generated sequences are predictable in order to remove this weakness of fcsr based generators we propose filtering the state of the fcsr with a linear function this method is efficient since the fcsr structure is not related to a linear property this paper presents an extensive study of fcsr automata a security analysis of our generator concerning linear and 2 adic cryptanalysis algebraic attack correlation attack etc and a practical example of parameters in order to design this generator an important point concerning this generator is the fact that it is simple and efficient both in hardware and software implementation

efficient methods of estimate correlation functions of gaussian processes and their performance analysis new efficient methods to estimate crosscorrelation functions of gaussian signals are studied in these methods the covariance property of the gaussian distribution is utilized such that the correlation estimates can be computed with only additions to evaluate the performances of the methods exact expressions for the bias and variance of these estimators are formulated and utilized in comparing these methods with the conventional correlation estimator as a result we point out that these new methods can give estimates which are comparable to the conventional approach

on the odd and the aperiodic correlation properties of the kasami sequences derives a new upper bound for the odd and the aperiodic correlations of binary sequences in the small kasami family the approach is based on a technique described in s litsyn and a tietavainen 1994 that is originally due to i m vinogradov 1954 an essential ingredient in this method is a good upper bound on the discrete fourier coefficients of a shifted product of a pair of sequences the author obtains an upper bound of the order o spl radic llnl for the maximal aperiodic and odd correlation magnitudes for sequences of length l

correlation estimators based on simple nonlinear transformations the computational cost of estimating correlations may be reduced by employing sums of simple nonlinear functions of the data a quadruplex transformation is presented and the performance of the associated estimator is analyzed for real and complex gaussian processes with independent observations the variance of the estimator is approximately 14 higher than that obtained by averaging lag products

compression mappings on primitive sequences over z p sup e let z p sup e be the integer residue ring with odd prime p spl ges 5 and integer e spl ges 2 for a sequence a over z p sup e there is a unique p adic expansion a a sub 0 a spl middot p a sub e 1 spl middot p sup e 1 where each a sub i is a sequence over 0 1 p 1 and can be regarded as a sequence over the finite field gf p naturally let f x be a primitive polynomial over z p sup e and g f x p sup e the set of all primitive sequences generated by f x over z p sup e set spl phi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 1 x sub 0 x sub 1 x sub e 2 spl psi sub e 1 x sub 0 x sub e 1 x sub e 1 sup k spl eta sub e 2 2 x sub 0 x sub 1 x sub e 2 where spl eta sub e 2 1 and spl eta sub e 2 2 are arbitrary functions of e 1 variables over gf p and 2 spl les k spl les p 1 then the compression mapping spl phi sub e 1 g f x p sup e spl rarr gf p sup spl infin a spl rarr spl phi sub e 1 a sub 0 a sub e 1 is injective that is a b if and only if spl phi sub e 1 a sub 0 a sub e 1 spl phi sub e 1 b sub 0 b sub e 1 for a b spl isin g f x p sup e furthermore if f x is a strongly primitive polynomial over z p sup e then spl phi sub e 1 a sub 0 a sub e 1 spl psi sub e 1 b sub 0 b sub e 1 if and only if a b and spl phi sub e 1 x sub 0 x sub e 1 spl psi sub e 1 x sub 0 x sub e 1 for a b spl isin g f x p sup e

the most significant bit of maximum length sequences over spl zopf 2 sup l autocorrelation and imbalance the imbalance and the autocorrelation of the binary sequences in the title are explored by combining the local weil bound with spectral analysis recent estimates on these quantities are improved by a factor of order 2 sup l 2 for large l

optimal biphase sequences with large linear complexity derived from sequences over z sub 4 new families of biphase sequences of size 2 sup r 1 1 r being a positive integer are derived from families of interleaved maximal length sequences over z sub 4 of period 2 2 sup r 1 these sequences have applications in code division spread spectrum multiuser communication systems the families satisfy the sidelnikov bound with equality on spl theta sub max which denotes the maximum magnitude of the periodic cross correlation and out of phase autocorrelation values one of the families satisfies the welch bound on spl theta sub max with equality the linear complexity and the period of all sequences are equal to r r 3 2 and 2 2 sup r 1 respectively with an exception of the single m sequence which has linear complexity r and period 2 sup r 1 sequence imbalance and correlation distributions are also computed

on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers let m be a square free odd integer and z m the integer residue ring modulo m this paper studies the distinctness of primitive sequences over z m modulo 2 recently for the case of m pq a product of two distinct prime numbers p and q the problem has been almost completely solved as for the case that m is a product of more prime numbers the problem has been quite resistant to proof in this paper a partial proof is given by showing that a class of primitive sequences of order 2n 1 over z m is distinct modulo 2 where n is a positive integer besides as an independent interest this paper also involves two distribution properties of primitive sequences over z m which are related closely to our main results

on a fast digital method of estimating the autocorrelation of a gaussian stationary process the zero mean stationary gaussian processes have the property that if they are input into an instantaneous nonlinear device the cross correlation of input and output is proportional to the auto correlation of the input this suggests an estimation procedure for the autocorrelation function based mainly on additions which is a modified type of the pcc polarity coincidence correlator the object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties as a reference some examples are provided which compare the behavior of the modified ppc estimator to the classical one based on products and additions

incomplete exponential sums over galois rings with applications to some binary sequences derived from z sub 2 sup l an upper bound for the incomplete exponential sums over galois rings is derived explicitly based on the incomplete exponential sums we analyze the partial period properties of some binary sequences derived from z sub 2 sup l in detail such as the kerdock code binary sequences and the highest level sequences of primitive sequences over z sub 2 sup l the results show that the partial period distributions and the partial period independent r pattern distributions of these binary sequences are asymptotically uniform nontrivial upper bounds for the aperiodic autocorrelation of these sequences are also given

efficient autocorrelation estimation using relative magnitudes the relative magnitude estimator computes the normalized autocorrelation of a stationary gaussian process using simple nonlinear functions to eliminate most multiplications approximate expressions for bias and variance of the estimate are presented along with the results of a computer simulation the estimator performs well when compared to similar techniques

on the distinctness of modular reductions of maximal length sequences modulo odd prime powers we discuss the distinctness problem of the reductions modulo m of maximal length sequences modulo powers of an odd prime p where the integer m has a prime factor different from p for any two different maximal length sequences generated by the same polynomial we prove that their reductions modulo m are distinct in other words the reduction modulo m of a maximal length sequence is proved to contain all the information of the original sequence

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

applications of the α relation to krasner hyperrings abstract this paper deals with a special type of hyperrings called krasner hyperring the main tool is the studding of the relation the relation was introduced by davvaz and vougiouklis indeed we use the relation in a given krasner hyperring in this way the relation is the smallest equivalence relation on a krasner hyperring r such that r is a commutative ring results are obtained on krasner hyperrings derived hyperrings and parts

fully simple semihypergroups transitive digraphs and sequence a000712 abstract fully simple semihypergroups have been introduced in 9 motivated by the study of the transitivity of the fundamental relation in semihypergroups here we determine a transversal of isomorphism classes of fully simple semihypergroups with a right absorbing element the structure of that transversal can be described by means of certain transitive acyclic digraphs moreover we prove that if n is an integer 2 then the number of isomorphism classes of fully simple semihypergroups of size n 1 with a right absorbing element is the n 1 th term of sequence a000712 in 20 namely k 0 n p k p n k where p k denotes the number of nonincreasing partitions of integer k

nilpotent groups derived from hypergroups in this paper we introduce the smallest equivalence relation on a hypergroup h such that the quotient h the set of all equivalence classes is a nilpotent group the characterization of nilpotent groups via strongly regular relations is investigated and several results on the topic are presented

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

construction of n ary f polygroups by an n ary f hyperoperation on a non empty set a we mean a function from a a to the set of all non zero fuzzy subsets of a where a appears n times using this concept we introduce the notion of n ary f polygroups which is a generalization of ideas presented by zahedi hasankhani and davvaz et al some basic results are obtained

period distribution of generalized discrete arnold cat map for n p e in this paper we analyze the period distribution of the generalized discrete cat map over the galois ring where is a prime the sequences generated by this map are modeled as 2 dimensional lfsr sequences employing the generation function and the hensel lifting approaches full knowledge of the detail period distribution is obtained analytically our results not only characterize the period distribution of the cat map which gives insights to various applications but also demonstrate some approaches to deal with the period of a polynomial in the galois ring

an efficient technique for high correlation estimation two sum based estimators are proposed as fast accurate methods for estimating the normalized acf of stationary processes for gaussian processes their performances are evaluated in terms of bias and covariance and are compared to the ones of the conventional direct estimator and of the hybrid sign and the polarity coincidence fast methods for high correlation values the proposed estimators exhibit the same accuracy as the direct estimator

transposition hypergroups noncommutative join spaces the study of various kinds of algebraic hypergroups is unified in the theory of transposition hypergroups the hyperoperation in any hypergroup has two inverses given bya b x a xb andb a x a bx a transposition hypergroup is a hypergroup where transposition b a c d impliesad bc holds the algebra of transposition hypergroups is developed closed subhypergroupsnthat are reflexive a n n a have distinguished structural significance the quotient space of a transposition hypergroup modulo a reflexive closed subhypergroup forms a transposition hypergroup that is a polygroup then generalizations of the isomorphism theorems and the jordan holder theorem of group theory are obtained

hyperrings and α relations a general approach abstract the study of the equivalence relations of particular multialgebras for which the factor multialgebras are universal algebras satisfying certain identities is a very important and intensively studied topic in multialgebra theory and not only our paper provides a general multialgebraic approach for the construction of all these relations and also some important and interesting properties concerning the construction of the corresponding factor universal algebra one of the purposes of our approach is to improve some results concerning relations of hyperrings and krasner hyperrings and we will do this in the last sections of this paper

a note on the computational complexity of high correlation estimators two fast estimators of correlation coefficients namely the absolute difference average ada and the relative magnitude rm correlators have been proposed as well suited for high correlation estimation it is shown that equivalent implementations of the ada estimators actually require the same number of additions and comparisons as the rm estimator the computational costs of the two estimators are the same

products of fuzzy finite state machines abstract we introduce the concepts of fuzzy transformation semigroups coverings cascade and wreath products for fuzzy finite state machines in order to overcome some of the difficulties which arise from the fuzzification of these concepts we also introduce the notions of polysemigroups and weak coverings

arithmetic crosscorrelations of feedback with carry shift register sequences an arithmetic version of the crosscorrelation of two sequences is defined generalizing mandelbaum s 1967 arithmetic autocorrelations large families of sequences are constructed with ideal vanishing arithmetic crosscorrelations these sequences are decimations of the 2 adic expansions of rational numbers p q such that 2 is a primitive root module q

fuzzy n ary subpolygroups recently n ary hypergroups were introduced and analyzed by davvaz and vougiouklis n ary polygroups are suitable generalizations of polygroups and a special case of n ary hypergroups the aim of this paper is to introduce the notion of a fuzzy n ary subpolygroup of an n ary polygroup and to extend the fuzzy results of fundamental equivalence relations to n ary polygroups

further result of compressing maps on primitive sequences modulo odd prime powers let be the integer residue ring with odd prime and integer for a sequence over there is an unique adic expansion where each is a sequence over and can be regarded as a sequence over the prime field gf naturally let be a strongly primitive polynomial over and the set of all primitive sequences generated by over suppose that gf gf it is shown that any function in is an injective map from to gf and the derived sequences of different functions are also different that is if and only if and for and these injective functions in can be considered as good candidates for the keys of a stream cipher

fully simple semihypergroups abstract in this paper we consider the class of semihypergroups h such that all subsemihypergroups k h are simple and when k 3 the fundamental relation k is not transitive for these semihypergroups we prove that hyperproducts of elements in h have size 2 and the quotient semigroup h is trivial this last result allows us to completely characterize these semihypergroups in terms of a small set of simple semihypergroups of size 3 finally we solve a problem on strongly simple semihypergroups introduced in 11

further result on distribution properties of compressing sequences derived from primitive sequences over bf z p e let p be an odd prime number e an integer greater than 1 and z pe the integer residue ring modulo pe in this paper we obtain an improved result of the previous paper ieee trans inf theory 56 1 2010 555 563 on distribution properties of compressing sequences derived from primitive sequences over z pe it is shown that two primitive sequences and b generated by a strongly primitive polynomial f x over z pe are the same if there exist s z p and k z p such that the distribution of in their compressing sequences ae 1 a0 ae 2 and be 1 b0 be 2 is coincident at the positions t with t k where x0 xe 2 is an e variable polynomial over z p with the coefficient of xe 2p 1 x1p 1x0p 1 not equal to 1 e p 1 2 and is an m sequence over z p determined by f x and a compared with the previous result this gives a more precise characterization on the positions of a compressing sequence i e of the form ae 1 a0 ae 2 derived from a primitive sequence a over z pe that completely determines a in particular the result is also true for the highest level sequence ae 1 by taking x0 xe 2 0

soft polygroups soft set theory introduced by molodtsov has been considered as an effective mathematical tool for modeling uncertainties in this paper we initiate the study of algebraic hyperstructures of soft sets the concepts of soft polygroups normal soft polygroups soft subpolygroups and normal soft subpolygroups are introduced and some related properties are investigated furthermore we propose the homomorphism and isomorphism of soft polygroups and establish three isomorphism theorems for soft polygroups

partial period distribution of fcsr sequences klapper and goresky 1995 introduced feedback with carry shift register fcsr and presented a significant kind of fcsr sequences that is l sequences they showed that the number of 0s and 1s occurring in one of their periods are equal we discuss the partial period distribution of l sequences and show that when the periods become large the proportion of 1s resp 0s occurring in any of their partial periods approximates 50

algebraic feedback shift registers a general framework for the design of feedback registers based on algebra over complete rings is described these registers generalize linear feedback shift registers and feedback with carry shift registers basic properties of the output sequences are studied relations to the algebra of the underlying ring synthesis of the register from the sequence which has implications for cryptanalysis and basic statistical properties these considerations lead to security measures for stream ciphers analogous to the notion of linear complexity that arises from linear feedback shift registers we also show that when the underlying ring is a polynomial ring over a finite field the new registers can be simulated by linear feedback shift registers with small nonlinear filters

fuzzy n ary polygroups related to fuzzy points recently fuzzy n ary sub polygroups were introduced and studied by davvaz corsini and leoreanu fotea b davvaz p corsini v leoreanu fotea fuzzy n ary sub polygroups comput math appl 57 2008 141 152 now in this paper the concept of email protected q fuzzy n ary sub polygroups email protected email protected email protected email protected fuzzy n ary sub polygroups and fuzzy n ary sub polygroup with thresholds of an n ary polygroup are introduced and some characterizations are described also we give the definition of implication based fuzzy n ary sub polygroups in an n ary polygroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

on the aperiodic and odd correlations of the binary shanbhag kumar helleseth sequences a previously derived upper bound on hybrid sums over galois rings is combined with a method due to vinogradov 1954 to obtain an upper bound for the maximum aperiodic and odd correlations of the binary sequences constructed by shanbhag kumar and helleseth see proc 1995 ieee int symp on information theory 1995

random properties of the highest level sequences of primitive sequences over z 2 sup e using the estimates of the exponential sums over galois rings we discuss the random properties of the highest level sequences spl alpha sub e 1 of primitive sequences generated by a primitive polynomial of degree n over z 2 sup e first we obtain an estimate of 0 1 distribution in one period of spl alpha sub e 1 on the other hand we give an estimate of the absolute value of the autocorrelation function c sub n h of spl alpha sub e 1 which is less than 2 sup e 1 2 sup e 1 1 spl radic 3 2 sup 2e 1 2 sup n 2 2 sup e 1 for h spl ne 0 both results show that the larger n is the more random spl alpha sub e 1 will be

further results on the distinctness of binary sequences derived from primitive sequences modulo square free odd integers this paper studies the distinctness of primitive sequences over z m modulo 2 where m is an odd integer that is composite and square free and z m is the integer residue ring modulo m a new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f x over z m are pairwise distinct modulo 2 such result improves a recent result obtained in our previous paper and consequently the set of primitive sequences over z m that can be proven to be distinct modulo 2 is greatly enlarged

polygroups derived from cogroups abstract a polygroup is a completely regular reversible in itself multigroup in the sense of dresher and ore 4 these systems occur naturally in the study of algebraic logic 1 2 some algebraic and combinatorial properties were developed in 3 the question of whether or not q 2 group the class of double quotients of groups is the same as the class of all chromatic polygroups is important for many reasons in this paper double quotients of groups are constructed in a natural way from cogroups cogroups were introduced by eaton 5 in an attempt to axiomatize d hypergroups i e systems obtainable from groups by right coset decompositions with respect to not necessarily normal subgroups eaton s axioms apply only to finite systems utumi 7 formulated a general notion and gave an example of a cogroup not isomorphic to a d hypergroup utumi s scalar partition hypergroups appear in section 2 the main results in section 3 show that polygroups derivable from cogroups are chromatic and they include all double quotients of groups

methods for estimating the autocorrelation function of complex gaussian stationary processes new methods for estimating the autocorrelation function acf of a complex gaussian stationary process are presented these methods are based on a general invariance property for the autocorrelation of a common class of the above processes this property suggests estimation procedures based on magnitude hard limiting and phase quantization the procedures are an extension of the relay estimator currently employed for real processes the computational cost and the general properties of the methods are discussed in particular some estimators especially suited for very simple implementations are considered the performance of the complex hybrid sign estimator is evaluated and compared to that of the classical direct estimator the proposed methods are attractive for many applications in the field of digital signal processing

upper bound for a hybrid sum over galois rings with applications to aperiodic correlation of some q ary sequences an upper bound for a hybrid exponential sum over galois rings is derived this bound is then used to obtain an upper bound for the maximum aperiodic correlation of some sequence families over galois rings the bound is of the order of spl radic qlnq where q 1 is the period of the sequences

asymptotic mean and variance of gini correlation for bivariate normal samples this paper derives the asymptotic analytical forms of the mean and variance of the gini correlation gc with respect to samples drawn from bivariate normal populations the asymptotic relative efficiency are of the gini correlation to pearson s product moment correlation coefficient ppmcc is investigated under the normal assumptions to gain further insight into gc we also compare the gini correlation to other two closely related correlation coefficients namely the order statistics correlation coefficient oscc and spearman s rho sr theoretical and simulation results suggest that the performance of gc lies in between those of oscc and sr when estimating the correlation coefficient of the bivariate normal population the newly found theoretical results along with other desirable properties enable gc to be a useful alternative to the existing coefficients especially when one wants to make a trade off between the efficiency and robustness to monotone nonlinearity

distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers let a and b be primitive sequences over z pe with odd prime p and e 2 for certain compressing maps we consider the distribution properties of compressing sequences of a and b and prove that a b if the compressing sequences are equal at the times t such that t k where is a sequence related to a we also discuss the s uniform distribution property of compressing sequences for some compressing maps we have that there exist different primitive sequences such that the compressing sequences are s uniform we also discuss that compressing sequences can be s uniform for how many elements s

performances of the hybrid sign correlation coefficient estimator for gaussian stationary processes the hybrid sign estimator is a method of estimating the autocorrelation coefficient for gaussian stationary processes based on sums in this correspondence the features of such an estimator are examined both for uncorrelated pairs of samples and for correlated pairs with an assigned autocorrelation function of the process a generalized estimator is considered by varying the spacing between the pairs of samples the performances in terms of bias covariance and variance are given in simple approximate formulas and compared in comprehensive diagrams to the direct estimator based on sums of products and the polarity coincidence estimator based on counters

on a class of pseudorandom sequences from elliptic curves over finite fields following the idea of xing et al we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over finite fields in this correspondence with the help of the tool of exponential sums on elliptic curves we study their periods linear complexities linear complexity profiles distributions of r patterns periodic correlation partial period distributions and aperiodic correlation in detail the results show that they have nice randomness

minimal order semihypergroups of type u on the right ii abstract we prove a new characterization of the heart w h and of the derived d h of a finite semihypergroup h of type u on the right in terms of its hyperproducts consequently we characterize the minimal size of the proper semihypergroups h of type u on the right such that w h d h h w h d h h or w h d h h moreover we obtain new results on the fundamental relations and on finite semihypergroups of type u on the right in particular we prove that is transitive is transitive if h 8 and that there exist semihypergroups of type u on the right of size 9 where is not transitive hence the minimal size for a semihypergroup of type u on the right to have a nontransitive is 9

ordered regular equivalence relations on ordered semihypergroups abstract in this paper we introduce the concept of ordered regular strongly ordered regular equivalence relation on an ordered semihypergroup moreover we use hyperfilters to construct a strongly ordered regular equivalence relation on an ordered semihypergroup for which the corresponding quotient structure is a semilattice finally we construct an ordered regular equivalence relation on an ordered semihypergroup by hyperideals such that the corresponding quotient structure is also an ordered semihypergroup under a related order relation which is an answer to the open problem given by b davvaz p corsini and t changphas in european journal of combinatorics

further results on the distinctness of decimations of l sequences let alowbar be an l sequence generated by a feedback with carry shift register with connection integer pe where p is an odd prime and eges1 goresky and klapper conjectured that when pe notin 5 9 11 13 all decimations of alowbar are cyclically distinct when e 1 and p 13 they showed that the set of distinct decimations is large and in some cases all decimations are distinct in this article we further show that when eges2 and pene9 all decimations of alowbar are also cyclically distinct

isomorphism classes of the hypergroups of type u on the right of size five by means of a blend of theoretical arguments and computer algebra techniques we prove that the number of isomorphism classes of hypergroups of type u on the right of order five having a scalar bilateral identity is 14751 in this way we complete the classification of hypergroups of type u on the right of order five started in our preceding papers m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five far east j math sci 26 2 2007 393 418 m de salvo d freni g lo faro a new family of hypergroups and hypergroups of type u on the right of size five part two mathematicki vesnik 60 2008 23 45 m de salvo d freni g lo faro on the hypergroups of type u on the right of size five with scalar identity submitted for publication in particular we obtain that the number of isomorphism classes of such hypergroups is 14865

characterizations of strongly ordered regular relations on ordered semihypergroups abstract in this paper we give the fundamental normal homomorphism theorem of ordered semihypergroups moreover we characterize the strongly ordered regular relations on an ordered semihypergroup by means of the chain and obtain that the set of all strongly ordered regular relations on an ordered semihypergroup consists a complete lattice finally the subset of an ordered semihypergroup can serve as some ordered regular ordered semilattice relation class is determined

a lower bound on the linear span of an fcsr we have derived a lower bound on the linear span of a binary sequence generated by a feedback with carry shift register fcsr under the following condition q is a power of a prime such that q r sup e e spl ges 2 and r 2p 1 where both r and p are 2 prime this allows us to design fcsr stream ciphers similar to previously proposed linear feedback shift register lfsr stream ciphers

period and complementarity properties of fcsr memory sequences in this correspondence we investigate feedback with carry shift register fcsr memory sequences for an sequence generated by an fcsr with connection integer and initial memory we prove that for where and is the memory sequence generally speaking the period of a memory sequence is a factor of that of the fcsr output binary sequence we show there are a large number of connection integers with which an fcsr can generate sequences that have the same period as their memory sequences especially including all connection integers for sequences