Construction of self-dual codes with an automorphism of order p
- 주제(키워드) Automorphism , Extremal code , Self-dual code , Weight enumerator
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 AMER INST MATHEMATICAL SCIENCES
- 발행년도 2011
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000091913
- 본문언어 영어
- Published As http://dx.doi.org/10.3934/amc.2011.5.23
초록/요약
We develop a construction method for finding self-dual codes with an automorphism of order p with c independent p-cycles. In more detail, we construct a self-dual code with an automorphism of type p- (c; f + 2) and length n+2 from a self-dual code with an automorphism of type p- (c; f) and length n, where an automorphism of type p- (c; f) is that of order p with c independent cycles and fixed points. Using this construction, we find three new inequivalent extremal self-dual [54; 27; 10] codes with an automorphism of type 7- (7; 5) and two new inequivalent extremal self-dual [58; 29; 10] codes with an automorphism of of type 7- (8; 2). We also obtain an extremal self-dual [40; 20; 8] code with an automorphism of type 3- (10; 10), which is constructed from an extremal self-dual [38; 19; 8] code of type 3- (10; 8), and at least 482 inequivalent extremal self-dual [58; 29; 10] codes with an automorphism of type 3- (18; 4), which is constructed from an extremal self-dual [54; 27; 10] code of type 3- (18; 0); we note that the extremality is preserved. © 2011 AIMS-SDU.
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