Constructions of Formally Self-Dual Codes Over Z(4) and Their Weight Enumerators
- 주제(키워드) Formally self-dual code , code over Z(4) , Lee weight enumerator , Gray map , non-linear extremal binary formally self-dual code
- 주제(기타) Computer Science, Information Systems; Engineering, Electrical & Electronic
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- 발행년도 2017
- URI http://www.dcollection.net/handler/ewha/000000149714
- 본문언어 영어
- Published As http://dx.doi.org/10.1109/TIT.2017.2761388
초록/요약
We present three explicit methods for construction of formally self-dual codes over Z(4). We characterize relations between Lee weight enumerators of formally self-dual codes of length n over Z(4) and those of length n + 2; the first two construction methods are based on these relations. The last construction produces free formally self-dual codes over Z(4). Using these three constructions, we can find free formally self-dual codes over Z(4), as well as non-free formally self-dual codes over Z(4) of all even lengths. We find free or non-free formally self-dual codes over Z(4) of lengths up to ten using our constructions. In fact, we obtain 46 inequivalent formally self-dual codes whose minimum Lee weights are larger than self-dual codes of the same length. Furthermore, we find 19 non-linear extremal binary formally self-dual codes of lengths 12, 16, and 20, up to equivalence, from formally self-dual codes over Z(4) by using the Gray map.
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