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Group convolutional codes
Error-block codes and poset metrics
1. | Centro Politécnico, UFPR, Caixa Postal 019081, Jd. das Américas, CEP 81531-990, Curitiba, PR, Brazil |
2. | Centro de Engenharias e Ciências Exatas, UNIOESTE, Av. Tarquínio Joslin dos Santos, 1300, CEP 85870-650, Foz do Igua¸cu, PR, Brazil |
3. | Imecc - Unicamp, CP 6065, CEP 13083-970, Campinas, SP, Brazil |
$ V = V_1 \oplus V_2 \oplus\ldots \oplus V_n.$
In this paper we endow $V$ with a poset metric such that the $P$-weight is constant on the non-null vectors of a component $V_i$, extending both the poset metric introduced by Brualdi et al. and the metric for linear error-block codes introduced by Feng et al.. We classify all poset block structures which admit the extended binary Hamming code $[8; 4; 4]$ to be a one-perfect poset block code, and present poset block structures that turn other extended Hamming codes and the extended Golay code $[24; 12; 8]$ into perfect codes. We also give a complete description of the groups of linear isometries of these metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset metric spaces. In particular, we obtain the group of linear isometries of the error-block metric spaces.
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