${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$ -Additive Cyclic Codes, Generator Polynomials, and Dual Codes
Joaquim Borges, Cristina Fernández-Córdoba, Roger Ten-Valls · IEEE Transactions on Information Theory · 2016
A ℤ2ℤ4-additive code C ⊆ ℤ2αx ℤ4βis called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ2and the set of ℤ4coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the ℤ4[x]-module ℤ2[x]/(xα- 1) x 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.