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Infinite families of MDR cyclic codes over Z(4) via constacyclic codes over Z(4)[u]/< u(2)-1 >

Title
Infinite families of MDR cyclic codes over Z(4) via constacyclic codes over Z(4)[u]/< u(2)-1 >
Authors
Han, NayoungKim, BohyunKim, BoranLee, Yoonjin
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2020
Journal Title
DISCRETE MATHEMATICS
ISSN
0012-365XJCR Link

1872-681XJCR Link
Citation
DISCRETE MATHEMATICS vol. 343, no. 3
Keywords
Cyclic codeMDR codeConstacyclic codeFrobenius non-chain ringGray map
Publisher
ELSEVIER
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We study alpha-constacyclic codes over the Frobenius non-chain ring R := Z(4)[u]/< u(2) - 1 > for any unit alpha of R. We obtain new MDR cyclic codes over Z(4) using a close connection between alpha-constacyclic codes over R and cyclic codes over Z(4). We first explicitly determine generators of all alpha-constacyclic codes over R of odd length n for any unit alpha of R. We then explicitly obtain generators of cyclic codes over Z(4) of length 2n by using a Gray map associated with the unit alpha. This leads to a construction of infinite families of MDR cyclic codes over Z(4), where a MDR code means a maximum distance with respect to rank code in terms of the Hamming weight or the Lee weight. We obtain 202 new cyclic codes over Z(4) of lengths 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50 and 54 by implementing our results in Magma software; some of them are also MDR codes with respect to the Hamming weight or the Lee weight. (C) 2019 Elsevier B.V. All rights reserved.
DOI
10.1016/j.disc.2019.111771
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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