An efficient construction of self-dual codes
- 주제(키워드) Building-up construction , Linear codes , Self-dual codes
- 관리정보기술 faculty
- 등재 SCIE, KCI등재, SCOPUS
- 발행기관 Korean Mathematical Society
- 발행년도 2015
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000115807
- 본문언어 영어
- Published As http://dx.doi.org/10.4134/BKMS.2015.52.3.915
초록/요약
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]. © 2015 Korean Mathematical Society.
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