A note on towers of function fields over finite fields

For a tower F 1 ⊆ F 2 ⊆ ⋯ of algebraic function fields F i/F q, define τ := lim i→∞ N(F i)/g(F i), where N(F i) is the number of rational places and g(F i) is the genus of F i/F q. The purpose of this note is to calculate A for a class of towers which was studied in [1], [2] and [3]

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units

Somitogenesis Clock-Wave Initiation Requires Differential Decay and Multiple Binding Sites for Clock Protein

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms

Codes on Fibre Products of Some Kummer Coverings

AbstractThe purpose of this paper is to construct fairly long geometric Goppa codes overFqwith rather good parameters by fibre products of some Kummer coverings. This paper also extends the results of Stepanov [1] and Stepanov and Özbudak [2]

Codes on superelliptic curves

The purpose of this paper is to apply superelliptic curves with a lot of rational points to construct rather good geometric Goppa codes. © TÜBİTAK

An improvement on the bounds of Weil exponential sums over Galois rings with some applications

10.1109/TIT.2004.834743IEEE Transactions on Information Theory50102529-2539IETT

A note on towers of function fields over finite fields

For a tower F 1 ⊆ F 2 ⊆ ⋯ of algebraic function fields F i/F q, define λ := lim i→∞ N(F i)/g(F i), where N(F i) is the number of rational places and g(F i) is the genus of F i/F q. The purpose of this note is to calculate λ for a class of towers which was studied in [1], [2] and [3]. Copyright © 1998 by Marcel Dekker, Inc

Constructions of digital nets using global function fields

Acta Arithmetica1053279-30

Improved p-ary codes and sequence families from Galois rings

Lecture Notes in Computer Science3486236-24

Improved p-ary codes and sequence families from galois rings of characteristic p2

10.1137/S089548010444506XSIAM Journal on Discrete Mathematics1941011-1028SJDM