MDS and near-MDS self-dual codes over large prime fields
Ilias Kotsireas, Christos Koukouvinos, Dimitris E. Simos · Advances in Mathematics of Communications · 2009
In this paper, we are interested in the construction of maximumdistance separable (MDS) self-dual codes over large prime fields that arise fromthe 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 variousprime 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 numberof 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 overprime fields give a better bound than the Pless-Pierce bound obtained from amodified Gilbert-Varshamov bound.