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In this paper, we develop a theory for constructing cyclic codes of odd length over the ring R = ℤ 4 + u ℤ 4 + v ℤ 4 , where u 2 = v 2 = u v = v u = 0 , which plays an important role in DNA computing. A direct link between the elements of R and the 6 4 codons used in the amino acids of the living organisms is established. Then, we investigate reversible cyclic codes and reversible complement cyclic codes of odd length over R. Moreover, we give some properties of binary images of the codons under the Gray map. Finally, two examples of cyclic codes over R with their minimum Hamming distance will be studied as well. [ABSTRACT FROM AUTHOR]

In this paper, we use a method inspired by the valuation theory to classify completely cyclic codes of length 3 p s over p m + u p m + u 2 p m . Then, we compute their separation parameters which was useful to compute the Hamming distance in [8]. [ABSTRACT FROM AUTHOR]

Motivated by a generalization of the football pool problem, we introduce additive cyclic codes over mixed alphabets of the form where , for distinct primes . We study their algebraic properties, generating sets, and duals. Additionally, we give examples of additive cyclic codes over the alphabet that have best-known or optimal parameters. [ABSTRACT FROM AUTHOR]

Let , where and . In this paper, minimum generating sets of cyclic codes over are given. A necessary and sufficient condition for cyclic codes over to be -free is obtained and a BCH-type bound on the minimum Hamming distance for them is also given. [ABSTRACT FROM AUTHOR]