AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES

Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with q ≡ 1 (mod 4), and over other certain...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2015, 52(3), , pp.915-923
Main Authors: Kim, Jon-Lark, Lee, Yoonjin
Format: Article
Language:English
Subjects:
수학
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Summary:Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with q ≡ 1 (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with q = pr ≡ 3 (mod 4) with an odd prime p satisfying p ≡ 3 (mod 4) with r odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual [16, 8, 7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24, 12, 9]. KCI Citation Count: 11
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.2015.52.3.915