$\mathbb {Z} _p\mathbb {Z} _p [v] $-Additive cyclic codes of length $(\alpha,\beta) $ can be
viewed as $ R [x] $-submodules of $\mathbb {Z} _p [x]/(x^\alpha-1)\times R [x]/(x^\beta-1) …

We construct a class of Z _p Z _p v Z p Z p v-additive cyclic codes, where p is a prime
number and v^ 2= vv 2= v. We determine the asymptotic properties of the relative minimum …

A binary linear code C is a Z _2 Z 2-double cyclic code if the set of coordinates can be
partitioned into two subsets such that any cyclic shift of the coordinates of both subsets …

Let p be an odd prime, q= pm, R= F q+ uF q with u 2= 1, and S= F q+ uF q+ vF q+ uvF q with
u 2= 1, v 2= 1, uv= vu. In this paper, F q RS-cyclic codes over F q RS are studied. As an …

Let q be a prime power with gcd (q, 6)= 1 gcd (q, 6)= 1. Let R= F _ q^ 2+ u F _ q^ 2+ v F _ q^
2+ uv F _ q^ 2 R= F q 2+ u F q 2+ v F q 2+ uv F q 2, where u^ 2= uu 2= u, v^ 2= vv 2= v and …

Recently some special type of mixed alphabet codes that generalize the standard codes has
attracted much attention. Besides Z 2 Z 4-additive codes, Z 2 Z 2 [u]-linear codes are …

In this paper we study Z 2 Z 4 Z 8-additive codes, which are extensions of recently
introduced Z 2 Z 4-additive codes. We determine the standard forms of the generator and …

Let p be an odd prime, q= pm, R 1= F q+ u F q+ v F q+ uv F q with u 2= 1, v 2= 1, uv= vu and
R 2= F q [u, v, w]/⟨ u 2-1, v 2-1, w 2-1, uv-vu, vw-wv, wu-uw⟩ with u 2= 1, v 2= 1, w 2= 1, uv …

We study the codes of the title by the CRT method, that decomposes such codes into
constituent codes, which are shorter codes over larger alphabets. Criteria on these …

The theory developed for ℤ 2 ℤ 4-additive codes is the starting point for much generalization
about codes over mixed alphabets. They have opened a new, emergent area of …