ℤ₂ℤ₄-additive codes as codes over rings

In this paper, it is shown that Z2Z4-additive codes with additional structure can be viewed as linear codes over rings. As an example, codes over the finite chain ring of order 8, R = (Formula Presented), which as additive group is isomorphic to Z2 × Z4, are shown to be Z2Z4-additive codes. Amongst other results connecting linear codes over R and their Z2Z4-additive images, it is shown that the Z2Z4-additive image of a cyclic code over R is separable, that is, a direct sum of a binary linear code and a linear code over Z4. The family of chain rings, (Formula Presented), where 1 ≤ t < s, and the finite commutative local Frobenius non-chain ring (Formula Presented) are also considered as alphabets for the study of Z2Z4-additive codes. © 2023 American Mathematical Society