American Institute of Mathematical Sciences

August  2012, 6(3): 287-303. doi: 10.3934/amc.2012.6.287

Characterization and constructions of self-dual codes over $\mathbb Z_2\times \mathbb Z_4$

 1 Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain 2 Department of Mathematics, University of Scranton, Scranton, PA 18510, United States

Received  March 2011 Revised  March 2012 Published  August 2012

Self-dual codes over $\mathbb Z_2\times\mathbb Z_4$ are subgroups of $\mathbb Z_2^\alpha\times\mathbb Z_4^\beta$ that are equal to their orthogonal under an inner-product that relates these codes to the binary Hamming scheme. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exist a self-dual code $\mathcal C\subseteq \mathbb Z_2^\alpha \times\mathbb Z_4^\beta$ are established. Moreover, the construction of such a code for each type and possible pair $(\alpha,\beta)$ is given. The standard techniques of invariant theory are applied to describe the weight enumerators for each type. Finally, we give a construction of self-dual codes from existing self-dual codes.
Citation: Joaquim Borges, Steven T. Dougherty, Cristina Fernández-Córdoba. Characterization and constructions of self-dual codes over $\mathbb Z_2\times \mathbb Z_4$. Advances in Mathematics of Communications, 2012, 6 (3) : 287-303. doi: 10.3934/amc.2012.6.287
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References:
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