Let p be an odd prime and q = p m , where m is a positive integer. We study the Θ t -cyclic and (Θ t , λ )-cyclic code over a finite commutative non-chain ring R = F q [u, v, w]/ u 2 = u, v 2 = v, w 2 = 1, uv = vu = 0, uw = wu, wv = vw , where λ is a unit in R.

In this work, we have investigated the one generator cyclic DNA codes with reverse and reverse complement constraints over the ring R = Z4 +uZ4 +u 2 Z4 with u 3 = 0. Skew cyclic codes with reverse complement constraint are constructed over R. We have also determined a one-to-one correspondence between the elements of the ring R and DNA codons satisfying the Watson-Crick complement. Finally, we have established some examples which satisfy the given constraints.

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In this correspondence, we investigate the covering radius of various types of repetition codes over Z p k ( k ≥ 2 ) with respect to the Lee distance. We determine the exact covering radius of the various repetition codes, which have been constructed using the zero divisors and units in Z p k . We also derive the lower and upper bounds on the covering radius of block repetition codes over Z p k .