New MDS or Near-MDS self-dual codes

T. Aaron Gulliver, Jon Lark Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

50 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

Bibliographical note

Funding Information:
Manuscript received January 8, 2008; revised June 11, 2008. Published August 27, 2008 (projected). The work of Y. Lee was supported by KOSEF under Grant R01-2008-000-11721-0. T.A. Gulliver is with the Department of of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC V8W 3P6, Canada (e-mail: agullive@ece.uvic.ca). J.-L. Kim is with the Department of Mathematics, University of Louisville, Louisville, KY 40292 USA (e-mail: jl.kim@louisville.edu). Y. Lee is with the Department of Mathematics, Ewha Womans University 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul, 120-750, Korea (e-mail: yoon-jinl@ewha.ac.kr). Communicated by T. Etzion, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2008.928297

Keywords

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

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