@article{8274ba30023944879989003e63185cac,
title = "New MDS or Near-MDS self-dual codes",
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.",
keywords = "Multiple description source (MDS) codes, Reed-Solomon (RS) codes, Self-dual codes",
author = "Gulliver, {T. Aaron} and Kim, {Jon Lark} and Yoonjin Lee",
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",
year = "2008",
doi = "10.1109/TIT.2008.928297",
language = "English",
volume = "54",
pages = "4354--4360",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "9",
}