Computer Science – Information Theory
Scientific paper
2007-10-05
Computer Science
Information Theory
This paper will be submitted to IEEE Trans. on Inform. Theory
Scientific paper
A code ${\cal C}$ is $\Z_2\Z_4$-additive if the set of coordinates can be partitioned into two subsets $X$ and $Y$ such that the punctured code of ${\cal C}$ by deleting the coordinates outside $X$ (respectively, $Y$) is a binary linear code (respectively, a quaternary linear code). In this paper $\Z_2\Z_4$-additive codes are studied. Their corresponding binary images, via the Gray map, are $\Z_2\Z_4$-linear codes, which seem to be a very distinguished class of binary group codes. As for binary and quaternary linear codes, for these codes the fundamental parameters are found and standard forms for generator and parity check matrices are given. For this, the appropriate inner product is deduced and the concept of duality for $\Z_2\Z_4$-additive codes is defined. Moreover, the parameters of the dual codes are computed. Finally, some conditions for self-duality of $\Z_2\Z_4$-additive codes are given.
Borges Joaquim
Fernandez Claudio
Pujol Jaume
Rifá Josep
Villanueva Merce
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