Computing Efficiently a Parity-Check Matrix for Z<italic>ps</italic>-Additive Codes

Cristina Fernandez-Cordoba, Adrian Torres, Carlos Vela, Merce Villanueva

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Resum

he Z<italic>ps</italic> -additive codes of length <italic>n</italic> are subgroups of Z<italic>n ps</italic>, with <italic>p</italic> prime and <italic>s</italic> &#x2265; 1. They can be seen as a generalization of linear codes over Z2, Z4, or more general over Z2<italic>s</italic>. In this paper, we show two methods for computing a parity-check matrix of a Z<italic>ps</italic> -additive code from a generator matrix of the code in standard form. We also compare the performance of our results implemented in Magma with the current available function in Magma for linear codes over finite rings in general. Complementing this comparison, we also show a time complexity analysis of the algorithms. The rings Z<italic>ps</italic> belong to a more general class of rings: finite chain rings. Along the paper, we observe that the same results can be applied to any linear code over a finite commutative chain ring.
Idioma originalAnglès
Pàgines (de-a)1-1
Nombre de pàgines1
RevistaIEEE Transactions on Information Theory
DOIs
Estat de la publicacióPublicada - 18 de març 2024

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