A1 Refereed original research article in a scientific journal
Weighted codes in Lee metrics
Authors: Dorbec P, Gravier S, Honkala I, Mollard M
Publisher: SPRINGER
Publication year: 2009
Journal: Designs, Codes and Cryptography
Journal name in source: DESIGNS CODES AND CRYPTOGRAPHY
Journal acronym: DESIGN CODE CRYPTOGR
Volume: 52
Issue: 2
First page : 209
Last page: 218
Number of pages: 10
ISSN: 0925-1022
DOI: https://doi.org/10.1007/s10623-009-9277-z(external)
Abstract
Perfect weighted coverings of radius one have been often studied in the Hamming metric. In this paper, we study these codes in the Lee metric. To simplify the notation, we use a slightly different description, yet equivalent. Given two integers a and b, an (a, b)-code is a set of vertices such that vertices in the code have a neighbours in the code and other vertices have b neighbours in the code. An (a, b)-code is exactly a perfect weighted covering of radius one with weight (b-a/b, 1/b). In this paper, we prove results of existence as well as of non-existence for (a, b)-codes on the multidimensional grid graphs.
Perfect weighted coverings of radius one have been often studied in the Hamming metric. In this paper, we study these codes in the Lee metric. To simplify the notation, we use a slightly different description, yet equivalent. Given two integers a and b, an (a, b)-code is a set of vertices such that vertices in the code have a neighbours in the code and other vertices have b neighbours in the code. An (a, b)-code is exactly a perfect weighted covering of radius one with weight (b-a/b, 1/b). In this paper, we prove results of existence as well as of non-existence for (a, b)-codes on the multidimensional grid graphs.
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