A1 Journal article – refereed

ON THE NORMALITY OF MULTIPLE COVERING CODES

List of Authors: HONKALA I

Publisher: ELSEVIER SCIENCE BV

Publication year: 1994

Journal: Discrete Mathematics

Journal name in source: DISCRETE MATHEMATICS

Journal acronym: DISCRETE MATH

Volume number: 125

Issue number: 1-3

Number of pages: 11

ISSN: 0012-365X

DOI: http://dx.doi.org/10.1016/0012-365X(94)90164-3

Abstract

A binary code C of length n is called a mu-fold r-covering if every binary word of length n is within Hamming distance r of at least mu codewords of C. The normality and the amalgamated direct sum (ADS) construction of 1-fold coverings have been extensively studied. In this paper we generalize the concepts of subnormality and normality to p-fold coverings and discuss how the ADS construction can be applied to them. In particular, we show that for r = 1, 2 all binary linear mu-fold r-coverings of length at least 2r + 1 and mu-fold normal.

A binary code C of length n is called a mu-fold r-covering if every binary word of length n is within Hamming distance r of at least mu codewords of C. The normality and the amalgamated direct sum (ADS) construction of 1-fold coverings have been extensively studied. In this paper we generalize the concepts of subnormality and normality to p-fold coverings and discuss how the ADS construction can be applied to them. In particular, we show that for r = 1, 2 all binary linear mu-fold r-coverings of length at least 2r + 1 and mu-fold normal.