Butson full propelinear codes

Armario, José Andrés ; Bailera, Ivan (Universidad de Zaragoza) ; Egan, Ronan

Resumen: 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.

Idioma: Inglés

DOI: 10.1007/s10623-022-01110-7

Año: 2022

Publicado en: DESIGNS CODES AND CRYPTOGRAPHY 91 (2022), 333–351
ISSN: 0925-1022

Factor impacto JCR: 1.6 (2022)

Categ. JCR: MATHEMATICS, APPLIED rank: 105 / 267 = 0.393 (2022) - Q2 - T2
Categ. JCR: COMPUTER SCIENCE, THEORY & METHODS rank: 64 / 111 = 0.577 (2022) - Q3 - T2

Factor impacto CITESCORE: 2.8 - Mathematics (Q2) - Computer Science (Q3)

Factor impacto SCIMAGO: 1.033 - Applied Mathematics (Q1) - Theoretical Computer Science (Q1) - Discrete Mathematics and Combinatorics (Q1) - Computer Science Applications (Q1)

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2019-104664GB-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)