120061 20240319081012.0 doi 10.1007/s10623-022-01110-7 sideral 130844 ART-2022-130844 eng Armario, José Andrés Butson full propelinear codes 2022 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/AEI/PID2019-104664GB-I00 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.6 2022 MATHEMATICS, APPLIED 105 / 267 = 0.393 2022 Q2 T2 COMPUTER SCIENCE, THEORY & METHODS 64 / 111 = 0.577 2022 Q3 T2 1.033 2022 Applied Mathematics 2022 Q1 Theoretical Computer Science 2022 Q1 Discrete Mathematics and Combinatorics 2022 Q1 Computer Science Applications 2022 Q1 2.8 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Bailera, Ivan Universidad de Zaragoza (orcid)0000-0001-6772-4802 Egan, Ronan 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 91 (2022), 333–351 Designs codes cryptogr. DESIGNS CODES AND CRYPTOGRAPHY 0925-1022 392541 http://zaguan.unizar.es/record/120061/files/texto_completo.pdf Versión publicada 1065762 http://zaguan.unizar.es/record/120061/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:120061 articulos driver 2024-03-18-15:13:59 ARTICLE