On ZpZp[u, v]-additive cyclic and constacyclic codes
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Let Z_p be the ring of residue classes modulo a prime p. The Z_pZ_p[u,v]-additive cyclic codes of length (α,β) is identify as Z_p[u,v][x]-submodule of Z_p[x]/〈 x^α-1〉×Z_p[u,v][x]/〈 x^β-1〉 where Z_p[u,v]=Z_p+uZ_p+vZ_p with u^2=v^2=uv=vu=0. In this article, we obtain the complete sets of generator polynomials, minimal generating sets for cyclic codes with length β over Z_p[u,v] and Z_pZ_p[u,v]-additive cyclic codes with length (α,β) respectively. We show that the Gray image of Z_pZ_p[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 Z_p. Moreover, some structural properties like generating polynomials, minimal generating sets of Z_pZ_p[u,v]-additive constacyclic code with length (α,p-1) are determined.
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