Construction of cyclic codes over GF (4) for DNA computing

Taher Abualrub; Ali Ghrayeb; Xiang Nian Zeng

doi:10.1016/j.jfranklin.2006.02.009

Construction of cyclic codes over GF (4) for DNA computing

Taher Abualrub^*, Ali Ghrayeb, Xiang Nian Zeng

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

63 Citations (Scopus)

Abstract

In this paper, we develop the theory for constructing linear and additive cyclic codes of odd length over GF (4) that are suitable for DNA computing. We call this class of codes reversible complement cyclic codes. We use this theory to study all such codes of lengths 7, 9, 11 and 13. We list the codes that have the largest number of codewords for a given minimum Hamming distance. We show that some of these codes have more codewords than previously known codes with the same minimum Hamming distance.

Original language	English
Pages (from-to)	448-457
Number of pages	10
Journal	Journal of the Franklin Institute
Volume	343
Issue number	4-5
DOIs	https://doi.org/10.1016/j.jfranklin.2006.02.009
Publication status	Published - Jul 2006
Externally published	Yes

Keywords

DNA computing
Hamming distance
Reversible complement cyclic codes

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10.1016/j.jfranklin.2006.02.009

Cite this

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title = "Construction of cyclic codes over GF (4) for DNA computing",

abstract = "In this paper, we develop the theory for constructing linear and additive cyclic codes of odd length over GF (4) that are suitable for DNA computing. We call this class of codes reversible complement cyclic codes. We use this theory to study all such codes of lengths 7, 9, 11 and 13. We list the codes that have the largest number of codewords for a given minimum Hamming distance. We show that some of these codes have more codewords than previously known codes with the same minimum Hamming distance.",

keywords = "DNA computing, Hamming distance, Reversible complement cyclic codes",

author = "Taher Abualrub and Ali Ghrayeb and \{Nian Zeng\}, Xiang",

year = "2006",

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journal = "Journal of the Franklin Institute",

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T1 - Construction of cyclic codes over GF (4) for DNA computing

AU - Abualrub, Taher

AU - Ghrayeb, Ali

AU - Nian Zeng, Xiang

PY - 2006/7

Y1 - 2006/7

N2 - In this paper, we develop the theory for constructing linear and additive cyclic codes of odd length over GF (4) that are suitable for DNA computing. We call this class of codes reversible complement cyclic codes. We use this theory to study all such codes of lengths 7, 9, 11 and 13. We list the codes that have the largest number of codewords for a given minimum Hamming distance. We show that some of these codes have more codewords than previously known codes with the same minimum Hamming distance.

AB - In this paper, we develop the theory for constructing linear and additive cyclic codes of odd length over GF (4) that are suitable for DNA computing. We call this class of codes reversible complement cyclic codes. We use this theory to study all such codes of lengths 7, 9, 11 and 13. We list the codes that have the largest number of codewords for a given minimum Hamming distance. We show that some of these codes have more codewords than previously known codes with the same minimum Hamming distance.

KW - DNA computing

KW - Hamming distance

KW - Reversible complement cyclic codes

UR - https://www.scopus.com/pages/publications/33747787670

U2 - 10.1016/j.jfranklin.2006.02.009

DO - 10.1016/j.jfranklin.2006.02.009

M3 - Article

AN - SCOPUS:33747787670

SN - 0016-0032

VL - 343

SP - 448

EP - 457

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 4-5

ER -

Construction of cyclic codes over GF (4) for DNA computing

Abstract

Keywords

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