Self-dual codes over ℤ 2×ℤ 4 are subgroups of ℤ α2×ℤ β4 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 α,β such that there exist a self-dual code C⊆ℤ α2×ℤ β4 are established. Moreover, the construction of such a code for each type and possible pair (α,β) 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. © 2012 AIMS.
|Journal||Advances in Mathematics of Communications|
|Publication status||Published - 1 Aug 2012|
- Self-dual codes
- Type I codes
- Type II codes
- Z xZ -additive codes 2 4