1. Construction of reversible cyclic codes over 𝔽q + u𝔽q + u2𝔽q
- Author
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Rehman Nadeem ur, Ahmad Mohammad Fareed, and Azmi Mohd
- Subjects
cyclic codes ,codes over rings ,hamming distance ,generator polynomial ,primary 94b15 ,secondary 94b05 ,Mathematics ,QA1-939 - Abstract
Let q be a power of prime p. In this article, we investigate the reversible cyclic codes of arbitrary length n over the ring R = 𝔽q +u𝔽q + u2𝔽q, where u3 = 0 mod q. Further, we find a unique set of generators for cyclic codes over R and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over R is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.
- Published
- 2023
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