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

Joaquim Borges; Steven T. Dougherty; Cristina Fernández-Córdoba

doi:10.3934/amc.2012.6.287

Article Contents

2012, Volume 6, Issue 3: 287-303. Doi: 10.3934/amc.2012.6.287

This issue Previous Article Wet paper codes and the dual distance in steganography Next Article Secondary constructions of bent functions and their enforcement

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
2.
Department of Mathematics, University of Scranton, Scranton, PA 18510

Received: March 2011

Revised: March 2012

Published: August 2012

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Self-dual codes,
Type I codes,
Type II codes,
$\mathbb Z_2\mathbb Z_4$-additive codes.

Mathematics Subject Classification: Primary: 94B60; Secondary: 94B25.

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