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Critical Pairs for the Product Singleton Bound

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 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.
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Submitted on : Friday, February 19, 2016 - 7:49:14 AM
Last modification on : Saturday, December 4, 2021 - 3:43:12 AM
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  • HAL Id : hal-01276221, version 1



Diego Mirandola, Gilles Zémor. Critical Pairs for the Product Singleton Bound. WCC2015 - 9th International Workshop on Coding and Cryptography 2015, Apr 2015, Paris, France. ⟨hal-01276221⟩



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