Titlebook: Coding, Cryptography and Combinatorics; Keqin Feng,Harald Niederreiter,Chaoping Xing Conference proceedings 2004 Springer Basel AG 2004 DE

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Constructions of Nonbinary Codes Correcting ,-Symmetric Errors and Detecting All Unidirectional ErroIn this paper, based on residue rings of polynomials, we present a general construction for nonbinary codes capable of correcting . or fewer symmetric errors and detecting all unidirectional errors with the magnitude error criterion. Some new lower bounds for such codes are obtained from this general construction.

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On Certain Equations over Finite Fields and Cross-Correlations of m-SequencesWe study the number of solutions to certain equations over finite fields and show how this gives a family of four-valued cross-correlation functions of binary m-sequences. This new family includes both of the four-valued cross-correlations found by Niho.

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New Constructions of Constant-Weight CodesBy generalizing a propagation rule for binary constant-weight codes, we present three constructions of binary constant-weight codes. It turns out that our constructions produce binary constant-weight codes with good parameters.

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https://doi.org/10.1007/978-3-642-88157-2 elliptic modular curves, Shimura curves, or Drinfeld modular curves by appropriate reduction. In this paper we review the recursive asymptotically optimal towers constructed so far, discuss the reasons behind Elkies’ conjecture, present numerical evidence of this conjecture, and sketch Elkies’ proo

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