Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉
- 주제(키워드) Additive code , Chain ring , Gray map , Optimal code , Self-orthogonal code
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2022
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000183987
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.ffa.2021.101972
초록/요약
We find a building-up type construction method for self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉. Our construction produces self-orthogonal codes over Z4 with increased lengths and free ranks from given self-orthogonal codes over Z4 with smaller lengths and free ranks; in the most of the cases their minimum weights are also increased. Furthermore, any self-orthogonal code over Z4 with generator matrix subject to certain conditions can be obtained from our construction. Employing our construction method, we obtain at least 125 new self-orthogonal codes over Z4 up to equivalence; among them, there are 35 self-orthogonal codes which are distance-optimal. Furthermore, we have eight self-orthogonal codes, which are distance-optimal among all linear codes over Z4 with the same type. As a method, we use additive codes over the finite ring Z4[u]/〈u2+1〉 with generator matrices G satisfying GGT=O, and we use a new Gray map from Z4[u]/〈u2+1〉 to Z43 as well. © 2021 Elsevier Inc.
more