On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup>
© 2019 Elsevier B.V. Let p be an odd prime, s, m be positive integers, γ,λ be nonzero elements of the finite field F p m such that γ p s =λ. In this paper, we show that, for any positive integer η, the Hamming distances of all repeated-root λ-constacyclic codes of length ηp s can be determined by...
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th-cmuir.6653943832-636792019-03-18T02:23:54Z On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta Mathematics © 2019 Elsevier B.V. Let p be an odd prime, s, m be positive integers, γ,λ be nonzero elements of the finite field F p m such that γ p s =λ. In this paper, we show that, for any positive integer η, the Hamming distances of all repeated-root λ-constacyclic codes of length ηp s can be determined by those of certain simple-root γ-constacyclic codes of length η. Using this result, Hamming distances of all constacyclic codes of length 4p s are obtained. As an application, we identify all MDS λ-constacyclic codes of length 4p s . 2019-03-18T02:23:54Z 2019-03-18T02:23:54Z 2019-05-01 Journal 0012365X 2-s2.0-85061557336 10.1016/j.disc.2019.01.023 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85061557336&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63679 |
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Mathematics |
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Mathematics Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| description |
© 2019 Elsevier B.V. Let p be an odd prime, s, m be positive integers, γ,λ be nonzero elements of the finite field F p m such that γ p s =λ. In this paper, we show that, for any positive integer η, the Hamming distances of all repeated-root λ-constacyclic codes of length ηp s can be determined by those of certain simple-root γ-constacyclic codes of length η. Using this result, Hamming distances of all constacyclic codes of length 4p s are obtained. As an application, we identify all MDS λ-constacyclic codes of length 4p s . |
| format |
Journal |
| author |
Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta |
| author_facet |
Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta |
| author_sort |
Hai Q. Dinh |
| title |
On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| title_short |
On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| title_full |
On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| title_fullStr |
On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| title_full_unstemmed |
On the Hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| title_sort |
on the hamming distances of repeated-root constacyclic codes of length 4p <sup>s</sup> |
| publishDate |
2019 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85061557336&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63679 |
| _version_ |
1681425940232536064 |