Z2Z4 -Additive Cyclic Codes, Generator Polynomials, and Dual Codes

© 2016 IEEE. A Z2Z4 -additive code C ≤ Z2α × Z4β 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. These codes can be identified as submodules of the Z [x] -module Z2 [x]/(xα -1)× Z4 [x]/(xβ -1). The parameters of a Z2Z4 -additive cyclic code are stated in terms of the degrees of the generator polynomials of the code. The generator polynomials of the dual code of a Z2Z4 -additive cyclic code are determined in terms of the generator polynomials of the code C.