Reversible cyclic codes over some finite rings and their application to DNA codes

被引：9

作者：

Prakash, Om ^{[1
]}

Patel, Shikha ^{[1
]}

Yadav, Shikha ^{[1
]}

机构：

[1] Indian Inst Technol Patna, Dept Math, Patna 801106, Bihar, India

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2021年 / 40卷 / 07期

关键词：

Cyclic codes; Hamming distance; Generator polynomial; Reversible cyclic code; Reversible-complement cyclic code; Dual code;

D O I：

10.1007/s40314-021-01635-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a prime p and q = p(m), we study reversible cyclic codes of arbitrary length over a ring R = F-q + uF(q) where u(2) = 0mod q. First, we find a unique set of generators for cyclic codes over R followed by a classification of reversible cyclic codes concerning their generators. Further, we find the set of generators for dual codes, and then under certain conditions, it is shown that dual of reversible cyclic code over Z(2) + uZ(2) is reversible. Moreover, we discuss reversible-complement cyclic codes over F-8 + uF(8), which play a very significant role in DNA computing. Finally, to show the importance of these results, examples of reversible cyclic codes and DNA codes are provided.

引用

页数：17

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