Self-Dual Codes over Z_2xZ_4

Details Self-Dual Codes over Z_2xZ_4 Self-Dual Codes over Z_2xZ_4

2009-10-16

arxiv.org/abs/0910.3084v1

Computer Science

Information Theory

Submitted to Designs, Codes and Cryptography

Scientific paper

Self-dual codes over $\Z_2\times\Z_4$ are subgroups of $\Z_2^\alpha \times\Z_4^\beta$ 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 $\alpha,\beta$ such that there exist a code $\C\subseteq \Z_2^\alpha \times\Z_4^\beta$ are established. Moreover, the construction of a $\add$-linear code for each type and possible pair $(\alpha,\beta)$ is given. Finally, the standard techniques of invariant theory are applied to describe the weight enumerators for each type.

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