On covering radius of codes over ℤ2p

Abstract

In this paper, we gives lower and upper bounds on the covering radius of codes over [Formula: see text], where [Formula: see text] is a prime integer with respect to Lee distance. We also determine the covering radius of various Repetition codes over [Formula: see text], where [Formula: see text] is a prime integer.

On the Covering Radius of Codes over Z p k

“…Note that this is a short alternate proof of [Theorem 3.1, [12,13]]. The p 2 − p zero divisors of order p 2 in Z p k are given by α i p k−1 + α j p k−2 for all α i ∈ {0, 1, .…”

“…The Covering Radius for the codes with respect to the Lee distance was first investigated for the ring Z 4 by Aoki [11]. Later, working on the Covering Radius of codes the with respect to the Lee distance gained interest [6,12,13]. We are particulary interested to find the Covering Radius for Repetition Codes, Since the Covering Radius of the Repetition Codes simplifies the process of finding the Covering Radius for many existing codes.…”