Critical pairs for the Product Singleton Bound
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Centrum voor Wiskunde en Informatica [CWI] | |
| hal.structure.identifier | Universiteit Leiden = Leiden University | |
| dc.contributor.author | MIRANDOLA, Diego | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ZÉMOR, Gilles | |
| dc.date.created | 2015 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0018-9448 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Institute of Electrical and Electronics Engineers | |
| dc.title.en | Critical pairs for the Product Singleton Bound | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1109/TIT.2015.2450207 | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.identifier.arxiv | 1501.06419 | |
| bordeaux.journal | IEEE Transactions on Information Theory | |
| bordeaux.page | 4928-4937 | |
| bordeaux.volume | 61 | |
| bordeaux.issue | 9 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01261399 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01261399v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=IEEE%20Transactions%20on%20Information%20Theory&rft.date=2015&rft.volume=61&rft.issue=9&rft.spage=4928-4937&rft.epage=4928-4937&rft.eissn=0018-9448&rft.issn=0018-9448&rft.au=MIRANDOLA,%20Diego&Z%C3%89MOR,%20Gilles&rft.genre=article |
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