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arXiv · 0807.4247

Z2Z4-linear codes: rank and kernel

Cristina Fernandez-Cordoba·Jaume Pujol·Merce Villanueva
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Abstract

A code C is Z2Z4-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). In this paper, the rank and dimension of the kernel for Z2Z4-linear codes, which are the corresponding binary codes of Z2Z4-additive codes, are studied. The possible values of these two parameters for Z2Z4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a Z2Z4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a Z2Z4-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a Z2Z4-additive code for each possible pair (r,k) is given.

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Cristina Fernandez-Cordoba, Jaume Pujol, Merce Villanueva. 2009-06-04. Z2Z4-linear codes: rank and kernel. https://arxiv.org/abs/0807.4247

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