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On Codes Over R and its Bounds of Some kind of Block Repetition Codes in R

P Chella Pandian

Abstract


This correspondence determines the lower and upper bounds of the covering radius in some kind of block repetition codes over the finite ring R=Z_2 Z_*, where Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. For covering radii of binary and octonary block repetition code over R is also discussed. This leads to the convenient formulation of code and arrives at the bounds.
Keywords: block repetition codes; covering radius; different weight; finite ring.

Abstrak
Korespondensi ini menentukan batas bawah dan batas atas dari jari-jari penutup suatu kode blok perulangan pada gelanggang hingga R=Z_2 Z_*, dengan Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. Dibahas juga jari-jari kode blok perulangan biner dan oktonari atas R. Diperoleh rumus untuk kode dan batasnya.
Kata Kunci: kode blok perulangan; penutup jari-jari; berat yang berbeda; gelanggang hingga.

2020MSC: 11T71, 94B05, 11H71.

Keywords


block repetition codes; covering radius; different weight; finite ring.

References


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DOI: 10.15408/inprime.v4i2.27239

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