Partial permutation decoding for binary linear and Z4-linear Hadamard codes
In this paper, s-PD-sets of minimum size s + 1 for partial permutation decoding for the binary linear Hadamard code H_m of length 2^m , for all m ≥ 4 and 2 ≤ s ≤ floor(2^m/(1+m)) -1, are constructed. Moreover, recursive constructions to obtain s-PD-sets of size l ≥ s + 1 for H_{m+1} of length 2^(m+1...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:170825 |
| Acceso en línea: | https://ddd.uab.cat/record/170825 https://dx.doi.org/urn:doi:10.1007/s10623-017-0342-8 |
| Access Level: | acceso abierto |
| Palabra clave: | Automorphism group Permutation decoding PD-set Hadamard code Z4-linear code |
| Sumario: | In this paper, s-PD-sets of minimum size s + 1 for partial permutation decoding for the binary linear Hadamard code H_m of length 2^m , for all m ≥ 4 and 2 ≤ s ≤ floor(2^m/(1+m)) -1, are constructed. Moreover, recursive constructions to obtain s-PD-sets of size l ≥ s + 1 for H_{m+1} of length 2^(m+1), from an s-PD-set of the same size for H_m , are also described. These results are generalized to find s-PD-sets for the Z4 -linear Hadamard codes H_{γ,δ} of length 2^m , m = γ + 2δ - 1, which are binary Hadamard codes (not necessarily linear) obtained as the Gray map image of quaternary linear codes of type 2^γ 4^δ . Specifically, s-PD-sets of minimum size s + 1 for H_{γ,δ} , for all δ ≥ 3 and 2 ≤ s ≤ floor(2^(2δ-2)/δ)-1, are constructed and recursive constructions are described. |
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