Critical Pairs for the Product Singleton Bound
MIRANDOLA, Diego
Institut de Mathématiques de Bordeaux [IMB]
Centrum voor Wiskunde en Informatica [CWI]
Universiteit Leiden = Leiden University
Institut de Mathématiques de Bordeaux [IMB]
Centrum voor Wiskunde en Informatica [CWI]
Universiteit Leiden = Leiden University
MIRANDOLA, Diego
Institut de Mathématiques de Bordeaux [IMB]
Centrum voor Wiskunde en Informatica [CWI]
Universiteit Leiden = Leiden University
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Centrum voor Wiskunde en Informatica [CWI]
Universiteit Leiden = Leiden University
Language
en
Communication dans un congrès
This item was published in
WCC2015 - 9th International Workshop on Coding and Cryptography 2015, 2015-04-13, Paris. 2016
English Abstract
We characterize Product-MDS pairs of linear codes, i.e. pairs of codes C, D whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the code length and the dimensions dim ...Read more >
We characterize Product-MDS pairs of linear codes, i.e. pairs of codes C, D whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the code length and the dimensions dim C, dim D. We prove in particular, for C = D, that if the square of the code C has minimum distance at least 2, and (C, C) is a Product-MDS pair, then either C is a generalized Reed-Solomon code, or C is a direct sum of self-dual codes. In passing we establish coding-theory analogues of classical theorems of additive combinatorics.Read less <
English Keywords
Error-correcting codes
Schur-product codes
Product Singleton Bound
Origin
Hal imported