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Constructions of Formally Self-Dual Codes Over Z(4) and Their Weight Enumerators

Title
Constructions of Formally Self-Dual Codes Over Z(4) and Their Weight Enumerators
Authors
Yoo, JinjooLee, YoonjinKim, Boreum
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2017
Journal Title
IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN
0018-9448JCR Link1557-9654JCR Link
Citation
vol. 63, no. 12, pp. 7667 - 7675
Keywords
Formally self-dual codecode over Z(4)Lee weight enumeratorGray mapnon-linear extremal binary formally self-dual code
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
We present three explicit methods for construction of formally self-dual codes over Z(4). We characterize relations between Lee weight enumerators of formally self-dual codes of length n over Z(4) and those of length n + 2; the first two construction methods are based on these relations. The last construction produces free formally self-dual codes over Z(4). Using these three constructions, we can find free formally self-dual codes over Z(4), as well as non-free formally self-dual codes over Z(4) of all even lengths. We find free or non-free formally self-dual codes over Z(4) of lengths up to ten using our constructions. In fact, we obtain 46 inequivalent formally self-dual codes whose minimum Lee weights are larger than self-dual codes of the same length. Furthermore, we find 19 non-linear extremal binary formally self-dual codes of lengths 12, 16, and 20, up to equivalence, from formally self-dual codes over Z(4) by using the Gray map.
DOI
10.1109/TIT.2017.2761388
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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