Self-Dual Codes over Z_2xZ_4

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.

Submitted to Designs, Codes and Cryptography