Article
Butson full propelinear codes
Author/s | Armario Sampalo, José Andrés
Bailera, Iván Egan, Ronan |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2020 |
Deposit Date | 2021-06-28 |
Published in |
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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 ... 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. |
Funding agencies | Junta de Andalucía |
Project ID. | FQM-016 |
Citation | Armario Sampalo, J.A., Bailera, I. y Egan, R. (2020). Butson full propelinear codes. ArXiv.org, arXiv:2010.06206 |
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