Algebraic characterization of minimum weight codewords of cyclic codes

Daniel Augot

Algebraic characterization of minimum weight codewords of cyclic codes

Daniel Augot

Research output: Contribution to conference › Paper › peer-review

Abstract

We consider primitive cyclic codes of length n over GF(q), where n = q^m - 1, and for any such code with defining set I(C), we define a system of algebraic equations, S_I(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system S_I(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.

Original language	English
Publication status	Published - 1 Dec 1994
Event	Proceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw Duration: 27 Jun 1994 → 1 Jul 1994

Conference

Conference	Proceedings of the 1994 IEEE International Symposium on Information Theory
City	Trodheim, Norw
Period	27/06/94 → 1/07/94

Cite this

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title = "Algebraic characterization of minimum weight codewords of cyclic codes",

abstract = "We consider primitive cyclic codes of length n over GF(q), where n = qm - 1, and for any such code with defining set I(C), we define a system of algebraic equations, SI(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system SI(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.",

author = "Daniel Augot",

year = "1994",

month = dec,

day = "1",

language = "English",

note = "Proceedings of the 1994 IEEE International Symposium on Information Theory ; Conference date: 27-06-1994 Through 01-07-1994",

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T1 - Algebraic characterization of minimum weight codewords of cyclic codes

AU - Augot, Daniel

PY - 1994/12/1

Y1 - 1994/12/1

N2 - We consider primitive cyclic codes of length n over GF(q), where n = qm - 1, and for any such code with defining set I(C), we define a system of algebraic equations, SI(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system SI(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.

AB - We consider primitive cyclic codes of length n over GF(q), where n = qm - 1, and for any such code with defining set I(C), we define a system of algebraic equations, SI(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system SI(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.

M3 - Paper

AN - SCOPUS:0028699811

T2 - Proceedings of the 1994 IEEE International Symposium on Information Theory

Y2 - 27 June 1994 through 1 July 1994

ER -

Algebraic characterization of minimum weight codewords of cyclic codes

Abstract

Conference

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