TY - JOUR
T1 - ℤ₂ℤ₄-additive codes as codes over rings
AU - Fernandez Cordoba, Cristina
N1 - Publisher Copyright:
© 2023 American Mathematical Society.
PY - 2023
Y1 - 2023
N2 - 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
AB - 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
UR - http://www.scopus.com/inward/record.url?scp=85163131114&partnerID=8YFLogxK
U2 - 10.1090/conm/785/15781
DO - 10.1090/conm/785/15781
M3 - Article
SN - 0271-4132
VL - 785
SP - 133
EP - 150
JO - Contemporary Mathematics
JF - Contemporary Mathematics
ER -