New MDS or Near-MDS self-dual codes

T. Aaron Gulliver, Jon Lark Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

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 multiple description source (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.

Original languageEnglish
Pages (from-to)4354-4360
Number of pages7
JournalIEEE Transactions on Information Theory
Volume54
Issue number9
DOIs
StatePublished - 2008

Keywords

  • Multiple description source (MDS) codes
  • Reed-Solomon (RS) codes
  • Self-dual codes

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