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
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Centrum voor Wiskunde en Informatica [CWI]
Universiteit Leiden = Leiden University
Idioma
en
Article de revue
Este ítem está publicado en
IEEE Transactions on Information Theory. 2015, vol. 61, n° 9, p. 4928-4937
Institute of Electrical and Electronics Engineers
Resumen en inglés
We characterize product-maximum distance separable (PMDS) pairs of linear codes, i.e., pairs of codes C and D whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the ...Leer más >
We characterize product-maximum distance separable (PMDS) pairs of linear codes, i.e., pairs of codes C and D whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the code length and the dimensions dim C and 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 PMDS 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.< Leer menos
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