A1 Refereed original research article in a scientific journal
ON THE NORMALITY OF MULTIPLE COVERING CODES
Authors: HONKALA I
Publisher: ELSEVIER SCIENCE BV
Publication year: 1994
Journal: Discrete Mathematics
Journal name in source: DISCRETE MATHEMATICS
Journal acronym: DISCRETE MATH
Volume: 125
Issue: 1-3
First page : 229
Last page: 239
Number of pages: 11
ISSN: 0012-365X
DOI: https://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.
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