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arXiv · 0910.3084

Self-Dual Codes over Z_2xZ_4

J. Borges·S. T. Dougherty·C. Fernandez-Cordoba
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Abstract

Self-dual codes over $\Z_2\times\Z_4$ are subgroups of $\Z_2^α\times\Z_4^β$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values $α,β$ such that there exist a code $\C\subseteq \Z_2^α\times\Z_4^β$ are established. Moreover, the construction of a $\add$-linear code for each type and possible pair $(α,β)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.

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J. Borges, S. T. Dougherty, C. Fernandez-Cordoba. 2009-10-16. Self-Dual Codes over Z_2xZ_4. https://arxiv.org/abs/0910.3084

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