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Construction of extremal self-dual codes over Z8 and Z16

Title
Construction of extremal self-dual codes over Z8 and Z16
Authors
Kim B.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2016
Journal Title
Designs, Codes, and Cryptography
ISSN
0925-1022JCR Link
Citation
vol. 81, no. 2, pp. 239 - 257
Keywords
Code over a ringExtremal self-dual codeFree self-dual codeOptimal self-dual codeSelf-dual code
Publisher
Springer New York LLC
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We present a method of constructing free self-dual codes over Z8 and Z16 which are extremal or optimal with respect to the Hamming weight. We first prove that every (extremal or optimal) free self-dual code over Z2m can be found from a binary (extremal or optimal) Type II code for any positive integer m≥ 2. We find explicit algorithms for construction of self-dual codes over Z8 and Z16. Our construction method is basically a lifting method. Furthermore, we find an upper bound of minimum Hamming weights of free self-dual codes over Z2m. By using our explicit algorithms, we construct extremal free self-dual codes over Z8 and Z16 up to lengths 40. © 2015, Springer Science+Business Media New York.
DOI
10.1007/s10623-015-0137-8
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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