`a`
Advances in Mathematics of Communications (AMC)
 

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

Pages: 287 - 303, Volume 6, Issue 3, August 2012      doi:10.3934/amc.2012.6.287

 
       Abstract        References        Full Text (410.6K)       Related Articles       

Joaquim Borges - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)
Steven T. Dougherty - Department of Mathematics, University of Scranton, Scranton, PA 18510, United States (email)
Cristina Fernández-Córdoba - Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (email)

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.

Received: March 2011;      Revised: March 2012;      Available Online: August 2012.

 References