Skip to Main content Skip to Navigation
Conference papers

Algebraic Solutions of Newton's identities for cyclic codes

Daniel Augot 1
1 CODES - Coding and cryptography
Inria Paris-Rocquencourt
Abstract : This paper consider the use of Newton's identities for establishing properties of cyclic codes. The main tool is to consider these identities as equations, and to look for the properties of the solutions. First these equations have been considered as necessary conditions for establishing non existence properties of cyclic codes, such as the non existence of codewords of a given weight. The properties of these equations are studied, and the properties of the solution to the algebraic system are given. The main theorem is that codewords in a hamming sphere around a given word can be characterized by algebraic conditions. This theorem enables to describe the minimum codewords of a given cyclic codes, by algebraic conditions. The equations are solved using the Buchberger's algorithm for computing a Groebner basis. Examples are also given with alternant codes, and with a non linear code.
Complete list of metadata

Cited literature [4 references]  Display  Hide  Download

https://hal.inria.fr/inria-00509468
Contributor : Daniel Augot <>
Submitted on : Thursday, August 12, 2010 - 3:52:34 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on: : Saturday, November 13, 2010 - 2:39:45 AM

Files

proceedings.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Daniel Augot. Algebraic Solutions of Newton's identities for cyclic codes. 1998 Information Theory Workshop, Aug 1998, Killarney, Ireland. pp.49, ⟨10.1109/ITW.1998.706411⟩. ⟨inria-00509468⟩

Share

Metrics

Record views

390

Files downloads

294