Abstract
Covering radius of repetition codes over \(F_{2}+vF_{2}+v^2F_2\) with \(v^3=1\)
Highlights
For more than a decade, codes over finite rings have gotten much attention of researchers due the definition of Gray map [1–3]
The covering radius of binary linear codes were studied by Helleseth et al, [6]
The covering radius of codes over Z4 have been determined by using lee weight and Chinese Euclidean lee weight [10,11]
Summary
For more than a decade, codes over finite rings have gotten much attention of researchers due the definition of Gray map [1–3]. The covering radius of binary linear codes were studied by Helleseth et al, [6]. Covering radius of linear codes over F2 + uF2 with u2 = 0 was determined by using Lee distance, Chinese Euclidean distance, and Bachoc distance [7–9]. The covering radius of codes over Z4 have been determined by using lee weight and Chinese Euclidean lee weight [10,11]. Panchanathan et al, in [14] studied bounds on covering radius for various repetition codes with respect to different and similar length over F2 + uF2 + u2F2 with u3 = 0 using Lee weight and generalized Lee weight. The goal of this paper is to investigate the covering radius of repetition codes over the finite ring F2 + vF2 + v2F2 with v3 = 1
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