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An infinite family of Griesmer quasi-cyclic self-orthogonal codes
- Title
- An infinite family of Griesmer quasi-cyclic self-orthogonal codes
- Authors
- Kim, Bohyun; Lee, Yoonjin; Yoo, Jinjoo
- Ewha Authors
- 이윤진
- SCOPUS Author ID
- 이윤진
- Issue Date
- 2021
- Journal Title
- FINITE FIELDS AND THEIR APPLICATIONS
- ISSN
- 1071-5797
1090-2465
- Citation
- FINITE FIELDS AND THEIR APPLICATIONS vol. 76
- Keywords
- Griesmer code; Quasi-cyclic code; Self-orthogonal code; Gray map
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- Our aim for this paper is to find the construction method for quasi-cyclic self-orthogonal codes over the finite field F-pm. We first explicitly determine the generators of alpha-constacyclic codes over the finite Frobenius non-chain ring R-p,R-m = F-pm [u, v]/(u(2) = v(2) = 0, uv = vu), where m is a positive integer, alpha = a + ub + vc + uvd is a unit of R-p,R-m,R- a, b, c, d is an element of F-pm, and a is nonzero. We then find a Gray map from R-p,R-m[x]/(x(n) - alpha) (with respect to homogeneous weights) to F-pm [x]/(x(p3m+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 alpha-constacyclic codes over R-p,R-m of length n, which produces infinitely many quasi-cyclic self orthogonal codes over F-pm of length p(3m+1) and index p(3m). 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. (C) 2021 Published by Elsevier Inc.
- DOI
- 10.1016/j.ffa.2021.101923
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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