- Publication venue
- Publication date
- 16/05/2019
- Field of study
Let Zp​ be the ring of residue classes modulo a prime p. The
Zp​Zp​[u,v]-additive cyclic codes of length
(α,β) is identify as Zp​[u,v][x]-submodule of
Zp​[x]/⟨xα−1⟩×Zp​[u,v][x]/⟨xβ−1⟩ where
Zp​[u,v]=Zp​+uZp​+vZp​ with
u2=v2=uv=vu=0. In this article, we obtain the complete sets of
generator polynomials, minimal generating sets for cyclic codes with length
β over Zp​[u,v] and
Zp​Zp​[u,v]-additive cyclic codes with length
(α,β) respectively. We show that the Gray image of
Zp​Zp​[u,v]-additive cyclic code with length
(α,β) is either a QC code of length 4α with index 4 or a
generalized QC code of length (α,3β) over Zp​.
Moreover, some structural properties like generating polynomials, minimal
generating sets of Zp​Zp​[u,v]-additive constacyclic
code with length (α,p−1) are determined.Comment: It is submitted to the journa