New MDS or Near-MDS Self-Dual Codes

We construct new MDS or near-MDS self-dual codes over large finite fields. In particular we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2m (m 2) using a Reed-Solomon (RS) code and its extension. It turns out that this MDS self-dual code is an extended duadic code. We construct Euclidean self-dual near-MDS codes of length n = q - 1 over GF(q) from RS codes when q 1 (mod 4) and q 113. We also construct many new MDS self-dual codes over GF(p) of length 16 for primes 29 p 113. Finally we construct Euclidean/Hermitian self-dual MDS codes of lengths up to 14 over GF(q2) where q = 19, 23, 25, 27, 29.

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: T. Aaron Gulliver, Jon-Lark Kim, Yoonjin Lee
• Keywords: Self-dual, Self-dual Codes, Self-dual Mds Codes, TIT 2008