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Pàgina inicial > Articles > Articles publicats > On recursive constructions of Z2Z4Z8-linear Hadamard codes |
Data: | 2023 |
Resum: | The Z2Z4Z8-additive codes are subgroups of Z α1 2 × Z α2 4 × Z α3 8 . A Z2Z4Z8-linear Hadamard code is a Hadamard code, which is the Gray map image of a Z2Z4Z8-additive code. In this paper, we generalize some known results for Z2Z4-linear Hadamard codes to Z2Z4Z8-linear Hadamard codes with α1 ̸= 0, α2 ̸= 0, and α3 ̸= 0. First, we give a recursive construction of Z2Z4Z8- additive Hadamard codes of type (α1, α2, α3;t1, t2, t3) with t1 ≥ 1, t2 ≥ 0, and t3 ≥ 1. It is known that each Z4-linear Hadamard code is equivalent to a Z2Z4-linear Hadamard code with α1 ̸= 0 and α2 ̸= 0. Unlike Z2Z4-linear Hadamard codes, in general, this family of Z2Z4Z8-linear Hadamard codes does not include the family of Z4-linear or Z8-linear Hadamard codes. We show that, for example, for length 211, the constructed nonlinear Z2Z4Z8-linear Hadamard codes are not equivalent to each other, nor to any Z2Z4-linear Hadamard, nor to any previously constructed Z2s -Hadamard code, with s ≥ 2. Finally, we also present other recursive constructions of Z2Z4Z8-additive Hadamard codes having the same type, and we show that, after applying the Gray map, the codes obtained are equivalent to the previous ones. |
Ajuts: | Agencia Estatal de Investigación PID2019-104664GB-I00 Agencia Estatal de Investigación PID2022-137924NB-I00 Agencia Estatal de Investigación RED2022-134306-T Agència de Gestió d'Ajuts Universitaris i de Recerca 2020/FI-SDUR-00475 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00643 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Hadamard code ; Gray map ; Z2 Z4 Z8-linear code |
Publicat a: | Advances in mathematics of communications, (November 2023), ISSN 1930-5338 |
Postprint 31 p, 668.2 KB |