© 1963-2012 IEEE. A ℤ2ℤ4-additive code C ⊂ ℤα 2 × ℤ β 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ2 and the set of ℤ4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. We study the binary images of ℤ2ℤ4-additive cyclic codes. We determine all ℤ2ℤ4-additive cyclic codes with odd β whose Gray images are linear binary codes. In this case, it is shown that such binary codes are permutation equivalent (by the Nechaev permutation) to ℤ2-double cyclic codes. Finally, the generator polynomials of these binary codes are given.
- Cyclic codes over ℤ and ℤ 2 4
- Gray map
- Nechaev permutation
- ℤ ℤ -additive cyclic 2 4