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 language | English |
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| 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 |
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| City | Trodheim, Norw |
| Period | 27/06/94 → 1/07/94 |