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Designs, Codes and Cryptography

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01-08-2016

Construction of binary linear codes via rational function fields

Authors: Lingfei Jin, Haibin Kan

Published in: Designs, Codes and Cryptography | Issue 3/2017

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Abstract

By employing a certain multiplicative group in the rational function field and places of degree one and two, we present a construction of binary linear codes in this paper. One feature is that the minimum distance of the code is bounded via the Hurwitz genus formula of function fields. It turns out that many optimal and best-known binary linear codes are obtained through our construction.

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Grassl M.: Tables of linear codes and quantum codes online table available at www.codetables.de. Accessed Sept 2014.

Litsyn S., Rains E.M., Sloane N.J.A.: Table of nonlinear binary codes online table at http://www.eng.tau.ac.il/~litsyn/tableand/. Accessed Sept 2014.

Jin L., Xing C.: New binary codes from rational function fields. IEEE Trans. Inf. Theory 61, 60–65 (2015).MathSciNetCrossRef

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Title: Construction of binary linear codes via rational function fields
Authors: Lingfei Jin
Haibin Kan
Publication date: 01-08-2016
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 3/2017
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-016-0252-1

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Construction of binary linear codes via rational function fields

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