On the hamming distances of constacyclic codes of length 5p<sup>S</sup>
© 2013 IEEE. Let p be a prime, s, m be positive integers, and λ be a nonzero element of the finite field Fpm. In this paper, the algebraic structures of constacyclic codes of length 5~ps~(p≠5) are obtained, which provide all self-dual, self-orthogonal and dual containing codes. Moreover, the exact v...
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2020
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th-cmuir.6653943832-683512020-04-02T15:27:32Z On the hamming distances of constacyclic codes of length 5p<sup>S</sup> Hai Q. Dinh Xiaoqiang Wang Jirakom Sirisrisakulchai Computer Science Engineering Materials Science © 2013 IEEE. Let p be a prime, s, m be positive integers, and λ be a nonzero element of the finite field Fpm. In this paper, the algebraic structures of constacyclic codes of length 5~ps~(p≠5) are obtained, which provide all self-dual, self-orthogonal and dual containing codes. Moreover, the exact values of the Hamming distances of all such codes are completely determined. Among other results, we obtain the degrees of the generator polynomials of all MDS repeated-root constacyclic codes of arbitrary length. As applications, several new and optimal codes are provided. 2020-04-02T15:25:21Z 2020-04-02T15:25:21Z 2020-01-01 Journal 21693536 2-s2.0-85082018252 10.1109/ACCESS.2020.2976536 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082018252&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68351 |
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Chiang Mai University |
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Chiang Mai University Library |
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Thailand |
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CMU Intellectual Repository |
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Computer Science Engineering Materials Science |
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Computer Science Engineering Materials Science Hai Q. Dinh Xiaoqiang Wang Jirakom Sirisrisakulchai On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| description |
© 2013 IEEE. Let p be a prime, s, m be positive integers, and λ be a nonzero element of the finite field Fpm. In this paper, the algebraic structures of constacyclic codes of length 5~ps~(p≠5) are obtained, which provide all self-dual, self-orthogonal and dual containing codes. Moreover, the exact values of the Hamming distances of all such codes are completely determined. Among other results, we obtain the degrees of the generator polynomials of all MDS repeated-root constacyclic codes of arbitrary length. As applications, several new and optimal codes are provided. |
| format |
Journal |
| author |
Hai Q. Dinh Xiaoqiang Wang Jirakom Sirisrisakulchai |
| author_facet |
Hai Q. Dinh Xiaoqiang Wang Jirakom Sirisrisakulchai |
| author_sort |
Hai Q. Dinh |
| title |
On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| title_short |
On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| title_full |
On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| title_fullStr |
On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| title_full_unstemmed |
On the hamming distances of constacyclic codes of length 5p<sup>S</sup> |
| title_sort |
on the hamming distances of constacyclic codes of length 5p<sup>s</sup> |
| publishDate |
2020 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082018252&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68351 |
| _version_ |
1681426804343046144 |