000120061 001__ 120061 000120061 005__ 20240319081012.0 000120061 0247_ $$2doi$$a10.1007/s10623-022-01110-7 000120061 0248_ $$2sideral$$a130844 000120061 037__ $$aART-2022-130844 000120061 041__ $$aeng 000120061 100__ $$aArmario, José Andrés 000120061 245__ $$aButson full propelinear codes 000120061 260__ $$c2022 000120061 5060_ $$aAccess copy available to the general public$$fUnrestricted 000120061 5203_ $$aIn 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. 000120061 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2019-104664GB-I00 000120061 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000120061 590__ $$a1.6$$b2022 000120061 592__ $$a1.033$$b2022 000120061 591__ $$aMATHEMATICS, APPLIED$$b105 / 267 = 0.393$$c2022$$dQ2$$eT2 000120061 593__ $$aApplied Mathematics$$c2022$$dQ1 000120061 591__ $$aCOMPUTER SCIENCE, THEORY & METHODS$$b64 / 111 = 0.577$$c2022$$dQ3$$eT2 000120061 593__ $$aTheoretical Computer Science$$c2022$$dQ1 000120061 593__ $$aDiscrete Mathematics and Combinatorics$$c2022$$dQ1 000120061 593__ $$aComputer Science Applications$$c2022$$dQ1 000120061 594__ $$a2.8$$b2022 000120061 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000120061 700__ $$0(orcid)0000-0001-6772-4802$$aBailera, Ivan$$uUniversidad de Zaragoza 000120061 700__ $$aEgan, Ronan 000120061 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000120061 773__ $$g91 (2022), 333–351$$pDesigns codes cryptogr.$$tDESIGNS CODES AND CRYPTOGRAPHY$$x0925-1022 000120061 8564_ $$s392541$$uhttps://zaguan.unizar.es/record/120061/files/texto_completo.pdf$$yVersión publicada 000120061 8564_ $$s1065762$$uhttps://zaguan.unizar.es/record/120061/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000120061 909CO $$ooai:zaguan.unizar.es:120061$$particulos$$pdriver 000120061 951__ $$a2024-03-18-15:13:59 000120061 980__ $$aARTICLE