The weight spectrum of two families of Reed-Muller codes
dc.contributor.author | Carlet, Claude Michael | |
dc.contributor.author | Solé, Patrick | |
dc.date.accessioned | 2024-04-17T11:15:19Z | |
dc.date.available | 2024-04-17T11:15:19Z | |
dc.date.created | 2024-01-15T10:28:41Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0012-365X | |
dc.identifier.uri | https://hdl.handle.net/11250/3127008 | |
dc.description.abstract | We determine the weight spectra of the Reed-Muller codes RM (m− 3, m) for m ≥ 6 and RM (m − 4, m) for m ≥ 8. The technique used is induction on m, using that the sum of two weights in RM (r −1, m−1) is a weight in RM (r, m), and using the characterization by Kasami and Tokura of the weights in RM (r, m) that lie between its minimum distance 2m−r and the double of this minimum distance. We also de- rive the weights of RM (3, 8), RM (4, 9), by the same technique. We conclude with a conjecture on the weights of RM (m − c, m), where c is fixed and m is large enough. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Elsevier | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | The weight spectrum of two families of Reed-Muller codes | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | acceptedVersion | en_US |
dc.source.articlenumber | 113568 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | 10.1016/j.disc.2023.113568 | |
dc.identifier.cristin | 2226360 | |
dc.source.journal | Discrete Mathematics | en_US |
dc.identifier.citation | Discrete Mathematics. 346, 10, 113568. | en_US |
dc.source.volume | 346 | en_US |
dc.source.issue | 10 | en_US |
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