Algebraic characterization of minimum weight codewords of cyclic codes

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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.

Original languageEnglish
Publication statusPublished - 1 Dec 1994
EventProceedings of the 1994 IEEE International Symposium on Information Theory - Trodheim, Norw
Duration: 27 Jun 19941 Jul 1994

Conference

ConferenceProceedings of the 1994 IEEE International Symposium on Information Theory
CityTrodheim, Norw
Period27/06/941/07/94

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