MDS and near-MDS self-dual codes over large prime fields | Zendy

Ilias Kotsireas | Zendy; Christos Koukouvinos | Zendy; Dimitris E. Simos | Zendy

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MDS and near-MDS self-dual codes over large prime fields

Author(s) -

Ilias Kotsireas,

Christos Koukouvinos,

Dimitris E. Simos

Publication year - 2009

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2009.3.349

Subject(s) - mathematics , prime (order theory) , finite field , prime power , diophantine equation , dual (grammatical number) , combinatorics , separable space , discrete mathematics , minimum distance , mathematical analysis , art , literature

In this paper, we are interested in the construction of maximum distance separable (MDS) self-dual codes over large prime fields that arise from the solutions of systems of diophantine equations. Using this method we con-struct many self-dualMDS (or near-MDS) codes of lengths up to 16 over various prime fields GF(p), where p = 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193 and 197. In addition, a number of optimal codes are presented for many lengths up to 40 over small prime fields GF(p). Furthermore, our results on the minimum weight of self-dual codes over prime fields give a better bound than the Pless-Pierce bound obtained from a modified Gilbert-Varshamov bound. © 2009 AIMS-SDU

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