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Butson full propelinear codes
dc.creator | Armario Sampalo, José Andrés | es |
dc.creator | Bailera, Iván | es |
dc.creator | Egan, Ronan | es |
dc.date.accessioned | 2021-06-28T10:41:13Z | |
dc.date.available | 2021-06-28T10:41:13Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Armario Sampalo, J.A., Bailera, I. y Egan, R. (2020). Butson full propelinear codes. ArXiv.org, arXiv:2010.06206 | |
dc.identifier.uri | https://hdl.handle.net/11441/114900 | |
dc.description.abstract | In this paper we study Butson Hadamard matrices, and codes over finite rings coming from these matrices in logarithmic form, called BH-codes. We introduce a new morphism of Butson Hadamard matrices through a generalized Gray map on the matrices in logarithmic form, which is comparable to the morphism given in a recent note of Ó Catháin and Swartz. That is, we show how, if given a Butson Hadamard matrix over the kth roots of unity, we can construct a larger Butson matrix over the ℓth roots of unity for any ℓ dividing k, provided that any prime p dividing k also divides ℓ. We prove that a Zps -additive code with p a prime number is isomorphic as a group to a BH-code over Zps and the image of this BH-code under the Gray map is a BH-code over Zp (binary Hadamard code for p = 2). Further, we investigate the inherent propelinear structure of these codes (and their images) when the Butson matrix is cocyclic. Some structural properties of these codes are studied and examples are provided. | es |
dc.description.sponsorship | Junta de Andalucía FQM-016 | es |
dc.format | application/pdf | es |
dc.format.extent | 24 | es |
dc.language.iso | eng | es |
dc.publisher | Cornell University | es |
dc.relation.ispartof | ArXiv.org, arXiv:2010.06206 | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Cocycles | es |
dc.subject | Butson Hadamard matrices | es |
dc.subject | Gray map | es |
dc.subject | propelinear codes | es |
dc.title | Butson full propelinear codes | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) | es |
dc.relation.projectID | FQM-016 | es |
dc.relation.publisherversion | https://arxiv.org/abs/2010.06206 | es |
dc.identifier.doi | DOI: 10.1007/s10623-022-01110-7 | |
dc.journaltitle | ArXiv.org | es |
dc.publication.issue | arXiv:2010.06206 | es |
dc.contributor.funder | Junta de Andalucía | es |
Ficheros | Tamaño | Formato | Ver | Descripción |
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Butson full propelinear codes.pdf | 301.4Kb | [PDF] | Ver/ | |