Abstract
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 .
Highlights
Codes over finite fields have been studied since the inception of coding theory
For the Quaternary case, it was discussed in [6]. This motivated us to work on the Covering Radius of Repetition Codes over the ring Z pk
[11] If C is a linear code over Z pk of length n, size M and minimum Lee distance d, the
Summary
Codes over finite fields have been studied since the inception of coding theory. Due to the rich algebraic structure of rings, the codes over rings gained popularity during the seventies [1,2,3]. The Covering Radius for the codes with respect to the Lee distance was first investigated for the ring Z4 by Aoki [11]. Later, working on the Covering Radius of codes the with respect to the. For the Quaternary case, it was discussed in [6] This motivated us to work on the Covering Radius of Repetition Codes over the ring Z pk. The zero divisors of different orders are obtained here, which will not be in the case of Z4 In this correspondence, we have investigated the covering radius of the codes over Z pk (k ≥ 2). With respect to the Lee distance in relation to the codes obtained by the Gray map. We have concluded the paper with the future work that can be proceeded with
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