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Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉

Title
Self-orthogonal codes over Z4 arising from the chain ring Z4[u]/〈u2+1〉
Authors
Kim B.Han N.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2022
Journal Title
Finite Fields and their Applications
ISSN
1071-5797JCR Link
Citation
Finite Fields and their Applications vol. 78
Keywords
Additive codeChain ringGray mapOptimal codeSelf-orthogonal code
Publisher
Academic Press Inc.
Indexed
SCIE; SCOPUS scopus
Document Type
Article
Abstract
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.
DOI
10.1016/j.ffa.2021.101972
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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