An infinite family of Griesmer quasi-cyclic self-orthogonal codes
- 주제(키워드) Gray map , Griesmer code , Quasi-cyclic code , Self-orthogonal code
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000183876
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.ffa.2021.101923
초록/요약
Our aim for this paper is to find the construction method for quasi-cyclic self-orthogonal codes over the finite field Fpm. We first explicitly determine the generators of α-constacyclic codes over the finite Frobenius non-chain ring Rp,m=Fpm[u,v]/〈u2=v2=0,uv=vu〉, where m is a positive integer, α=a+ub+vc+uvd is a unit of Rp,m, a,b,c,d∈Fpm, and a is nonzero. We then find a Gray map from Rp,m[x]/〈xn−α〉 (with respect to homogeneous weights) to Fpm[x]/〈xp3m+1n−a〉 (with respect to Hamming weights), which is linear and preserves minimum weights. We present an efficient algorithm for finding the Gray images of α-constacyclic codes over Rp,m of length n, which produces infinitely many quasi-cyclic self-orthogonal codes over Fpm of length p3m+1 and index p3m. In particular, some family turns out to be “Griesmer” codes; these Griesmer quasi-cyclic self-orthogonal codes are “new” codes compared with previously known Griesmer codes of dimension 4. © 2021
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