bounds on the decoding error probability of binary linear codes via their spectra bounds on the error probability of maximum likelihood decoding of a binary linear code are considered the bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel the bounds derived are applied to a code with an average spectrum and the result is compared to the random coding exponent the author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound for the case of awgn channel the author shows that berlekamp s 1980 tangential bound can be improved but even this improved bound does not coincide with the random coding bound although it can be very close to it

tighter bounds on the error probability of fixed convolutional codes we introduce new upper bounds for the bit and burst error probabilities when a convolutional code is used for transmission over a binary input additive white gaussian noise awgn channel and the decoder performs maximum likelihood decoding the bounds are tighter than existing bounds and nontrivial also for signal to noise ratios below the computational cutoff rate

speech analysis synthesis method and apparatus therefor an impulse sequence of a pitch frequency is detected from a phase equalized prediction residual of an input speech signal s t and a quasi periodic impulse sequence is obtained by processing the impulse sequence so that a fluctuation in its pitch frequency is within an allowed limit range the magnitudes of the quasi periodic impulse sequence are so determined as to minimize an error between the waveform of a synthesized speech obtainable by exciting an all pole filter 18 with the quasi periodic impulse sequence and the waveform of a phase equalized speech obtainable by applying the input speech signal to a phase equalizing filter 5 preferably the quasi periodic impulse sequence is supplied to the all pole filter after being applied to a zero filter 10 in which it is given features of the prediction residual of the speech coefficients of the zero filter are also determined so that the error of the waveforms of the synthesized speech and the phase equalized speech is minimum

multiple fibers on rational elliptic surfaces our main result theorem 0 1 classifies multiple fibers on rational elliptic surfaces over algebraically closed fields of arbitrary characteristic one result of this is the existence in positive characteristics of tame multiple fibers of additive type for several of the kodaira fiber types for which no examples were previously known 0 introduction we work in this paper over an algebraically closed field k of arbitrary characteristic p an elliptic surface f x b is a fibration of a complete smooth surface x over a complete smooth curve b such that the generic fiber is a smooth curve of genus one it is natural to wonder what kind of special fibers arise we answer this in the case of rational surfaces giving as a result examples of tame multiple fibers of additive type for every p o and for all such types except ib b 4 cf 5 to our knowledge the only example heretofore recognized is of multiplicity 2 and kodaira type iox due to katsura ka l1 although since our results were obtained we have seen a preprint of katsura and ueno ku giving other examples mostly for p 7 2 3 and kodaira type not ib b 0 any special fiber is an effective divisor on x and so can be written as mf menjcj where each curve cj is reduced and irreducible and the coefficients are positive integers with g c d nj 1 the positive integer m is the rnultiplicity of the fiber mf which is said to be a multiple fiber whenever m 1 the form of the divisor f enjcj is very restricted such a divisor is an indecomposable curve of canonical type mu a topological classification of all such curves has been given by kodaira ko cf 5 we refer to the classes which arise in this classification as the kodaira fiber types more generally the kodaira type of the fiber mf is mt where t is the type of f over an algebraically closed field k it is known that any multiple fiber mf of multiplicity m on a surface x is of the form mt where t is a kodaira type and m is divisible by and in characteristic 0 equal to the order of the normal bundle ox f s of e pic f of f in x but the extent to which these conditions are sufficient for there to occur on some elliptic surface a multiple fiber of type mt is not known of particular interest to us here are the tame multiple fibers of additive type these being fibers mf of multiplicity m where pic f is the additive group ga of the ground field k and m equals the order in ga f ox f s of these are possible only if p the characteristic of k is positive since ga only then has ptorsion but their occurrence is poorly understood received by the editors march 21 1987 1980 mathematzcs subject classzficatzon 1985 re szon primary 14j25 14m20 14d99

logarithmic transformations of rigid analytic elliptic surfaces we give new examples of algebraic elliptic surfaces and non algebraic rigid analytic elliptic surfaces by means of logarithmic transformations in the complex analytic case it is known that all multiple fibers of elliptic surfaces are obtained by logarithmic transformations using rigid analytic geometry we construct similar transformations of elliptic surfaces over complete non archimedean valuation base fields these operations yield rigid analytic elliptic fibrations with multiple fibers when the resulting surface admits an ample line bundle we may algebraize the surface in the positive characteristic case we obtain new types of algebraic elliptic surfaces we also obtain a non algebraic rigid analytic surface the combination of whose invariants appears neither in the algebraic case nor in the complex analytic case

a new upper bound on the first event error probability for maximum likelihood decoding of fixed binary convolutional codes corresp an upper bound on the first event error probability for maximum likelihood decoding of fixed binary convolutional codes on the binary symmetric channel is derived the bound is evaluated for rate 1 2 codes and comparisons are made with simulations and with the bounds of viterbi van de meeberg and post in particular the new bound is significantly better than van de meeberg s bound for rates above r comp

a block decodable 1 8 runlength limited rate 8 12 code describes a d k 1 8 runlength limited rll rate 8 12 code with fixed codeword length 12 the code is block decodable a codeword can be decoded without knowledge of preceding or succeeding codewords the code belongs to the class of bounded delay block decodable bdb codes with one symbol 8 bits look ahead due to its format this code is particularly attractive for use in combination with error correcting codes such as reed solomon codes over the finite field gf 2 sup 8

period and index of genus one curves over global fields the period of a curve is the smallest positive degree of galois invariant divisor classes the index is the smallest positive degree of rational divisors we construct examples of genus one curves with prescribed period and index over a given global field as long as the characteristic of the field does not divide the period

on the brauer group of a surface artin and tate 15 5 1 have shown in 1966 the existence of a canonical skew symmetric pairing on the non p part of br x whose kernel is exactly the set of divisible elements it follows from this fact that if the non p part of br x is finite then its order is a square or twice a square a few years later manin published examples of rational surfaces that is surfaces birational over k to the projective plane with brauer groups equal to z 2z it is only in 1996 that the examples of manin were revisited by urabe who found a mistake in them for rational surfaces the brauer group is relatively easy to understand and urabe 16 remark after 1 17 showed improving on a result of milne 9 that the brauer group of a rational surface has order a square in 17 0 3 urabe then proves in full generality that when p 2 the 2 part of br x modulo its divisible subgroup has order a square thus to complete the proof of theorem 1 it remains to treat the case where p 2 and x k is not rational as we remarked above it was wrongly assumed for about 30 years that br x was not always a square our method of proof provides for any p that the 2 part of br x has order a square via the knowledge of the 2 part

the cassels tate pairing on polarized abelian varieties let a e be a principally polarized abelian variety defined over a global field k and let a be its shafarevich tate group let a nd denote the quotient of a by its maximal divisible subgroup cassels and tate constructed a nondegenerate pairing a nd a nd q z if a is an elliptic curve then by a result of cassels the pairing is alternating but in general it is only antisymmetric using some new but equivalent definitions of the pairing we derive general criteria deciding whether it is alternating and whether there exists some alternating nondegenerate pairing on a nd these criteria are expressed in terms of an element c a nd that is canonically associated to the polarization e in the case that a is the jacobian of some curve a down to earth version of the result allows us to determine effectively whether a if finite is a square or twice a square we then apply this to prove that a positive proportion in some precise sense of all hyperelliptic curves of even genus g 2 over q have a jacobian with nonsquare if finite for example it appears that this density is about 13 for curves of genus 2 the proof makes use of a general result relating global and local densities this result can be applied in other situations

logarithmic good reduction of abelian varieties let k be a field which is complete for a discrete valuation we prove a logarithmic version of the neron ogg shafarevich criterion if a is an abelian variety over k which is cohomologically tame then a has good reduction in the logarithmic setting i e there exists a projective log smooth model of a over mathcal o k this implies in particular the existence of a projective regular model of a generalizing a result of kunnemann the proof combines a deep theorem of gabber with the theory of degenerations of abelian varieties developed by mumford faltings chai et al

neron models lie algebras and reduction of curves of genus one let k be a discrete valuation field let ok denote the ring of integers of k and let k be the residue field of ok of characteristic p 0 let s specok let x k be a smooth geometrically connected projective curve of genus 1 over k denote by ek the jacobian of x k let x s and e s be the minimal regular models of x k and ek respectively in this article we investigate the possible relationships between the special fibers xk and ek in doing so we are led to study the geometry of the picard functor pic x s when x s is not necessarily cohomologically flat as an application of this study we are able to prove in full generality a theorem of gordon on the equivalence between the artin tate and birch swinnertondyer conjectures recall that when k is algebraically closed the special fibers of elliptic curves are classified according to their kodaira type which is denoted by a symbol t in i n n z 0 ii ii iii iii iv iv given a type t and a positive integer m we denote by mt the new type obtained from t by multiplying all the multiplicities of t by m when k is algebraically closed the relationships between the type of a curve of genus 1 and the type of its jacobian can be summarized as follows

on torsors under elliptic curves and serre s pro algebraic structures let mathcal o k be a complete discrete valuation ring with algebraically closed residue field of positive characteristic and field of fractions k let x k be a torsor under an elliptic curve a k over k x the proper minimal regular model of x k over s hbox spec mathcal o k and j the identity component of the neron model of mathrm pic x k k 0 we study the canonical morphism q mathrm pic 0 x s rightarrow j which extends the natural isomorphism on generic fibres we show that q is pro algebraic in nature with a construction that recalls serre s work on local class field theory furthermore we interpret our results in relation to shafarevich s duality theory for torsors under abelian varieties

estimations of the transfer functions of noncatastrophic convolutional encoders a computational method which allows us to upper bound the solution of a wide class of systems of linear recurrent equations is proposed this method is used to estimate the transfer functions of noncatastrophic convolutional encoders