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자연과학대학
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Optimal Binary Few-Weight Codes Using a Mixed Alphabet Ring and Simplicial Complexes
Title
Optimal Binary Few-Weight Codes Using a Mixed Alphabet Ring and Simplicial Complexes
Authors
Mondal
;
Nilay Kumar
;
Lee
;
Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진
Issue Date
2024
Journal Title
IEEE Transactions on Information Theory
ISSN
1894-9448
Citation
IEEE Transactions on Information Theory vol. 70, no. 7, pp. 4865 - 4878
Keywords
few-weight optimal code
;
minimal code
;
self-orthogonal code
;
Simplicial complex
;
strongly walk-regular graph
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
We construct several families of distance-optimal few-weight binary linear codes. As a method, we use the mixed alphabet ring Z2Z2[u], u2 = 0 (viewing Z2Z2[u] as a Z2[u]-module) and three suitable defining sets, each consisting of three simplicial complexes generated by a single maximal element to construct three different families of linear codes over Z2[u], u2 = 0. We explicitly determine their Lee weight distributions and study their Gray images to obtain our results. It turns out that most of the distance-optimal codes obtained in this paper are self-orthogonal and minimal as well. We emphasize that we find an infinite family of binary three-weight projective codes with new parameters, which produce strongly l-walk-regular graphs for every odd l ≥ 3. © 2024 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
DOI
10.1109/TIT.2024.3384067
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