DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)

DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)

© 2018 World Scientific Publishing Company. In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements R1 = 2 + u2 (u2 = 1) to be a reversible cyclic code. We also obtain the structure of cyclic DNA co...

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Main Authors: Hai Q. Dinh, Abhay Kumar Singh, Sukhamoy Pattanayak, Songsak Sriboonchitta
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85044723621&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/58814
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-588142018-09-05T04:32:53Z DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u) Hai Q. Dinh Abhay Kumar Singh Sukhamoy Pattanayak Songsak Sriboonchitta Mathematics © 2018 World Scientific Publishing Company. In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements R1 = 2 + u2 (u2 = 1) to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring R = 2[u,v]/(u2 - 1,v3 - v,uv - vu), which plays an important role in Computational Biology. Furthermore, we establish a direct link between the elements of ring R and 64 codons used in the amino acids of living organisms by introducing a Gray map from R to R1. Among others, binary images of cyclic codes over R are also investigated. As applications, some cyclic DNA codes over R using the Gray map are provided. 2018-09-05T04:32:53Z 2018-09-05T04:32:53Z 2018-04-01 Journal 17937159 17935245 2-s2.0-85044723621 10.1142/S1793524518500420 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85044723621&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58814
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Hai Q. Dinh
Abhay Kumar Singh
Sukhamoy Pattanayak
Songsak Sriboonchitta
DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
description © 2018 World Scientific Publishing Company. In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements R1 = 2 + u2 (u2 = 1) to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring R = 2[u,v]/(u2 - 1,v3 - v,uv - vu), which plays an important role in Computational Biology. Furthermore, we establish a direct link between the elements of ring R and 64 codons used in the amino acids of living organisms by introducing a Gray map from R to R1. Among others, binary images of cyclic codes over R are also investigated. As applications, some cyclic DNA codes over R using the Gray map are provided.
format Journal
author Hai Q. Dinh
Abhay Kumar Singh
Sukhamoy Pattanayak
Songsak Sriboonchitta
author_facet Hai Q. Dinh
Abhay Kumar Singh
Sukhamoy Pattanayak
Songsak Sriboonchitta
author_sort Hai Q. Dinh
title DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
title_short DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
title_full DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
title_fullStr DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
title_full_unstemmed DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- V, u v - V u)
title_sort dna cyclic codes over the ring<inf>2</inf>[ u, v ] / (u<sup>2</sup>- 1, v<sup>3</sup>- v, u v - v u)
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85044723621&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/58814
_version_ 1681425135696871424

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