Skip to Main content Skip to Navigation
Conference papers

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.
Document type :
Conference papers
Complete list of metadata

Cited literature [12 references]  Display  Hide  Download

https://hal.inria.fr/hal-01276221
Contributor : Jean-Pierre Tillich <>
Submitted on : Friday, February 19, 2016 - 7:49:14 AM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM
Long-term archiving on: : Saturday, November 12, 2016 - 11:25:17 PM

File

wcc15-tu3-1.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01276221, version 1

Collections

Citation

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⟩

Share

Metrics

Record views

110

Files downloads

273