Arazgol Ghajari, Kazem Khashyarmanesh: ${\Bbb Z}_p({\Bbb Z}_p+u{\Bbb Z}_p+u^2{\Bbb Z}_p)$-additive cyclic codes, 337-354

Abstract:

Let $\mathcal{R}={\Bbb Z}_p+u{\Bbb Z}_p+u^2{\Bbb Z}_p$ be a commutative ring with $u^3=u$ and $p$ is an odd prime. The ${\Bbb Z}_p\mathcal{R}$-additive cyclic codes can be considered as $\mathcal{R}[x]$-submodules of $\frac{{\Bbb Z}_p[x]}{<x^\alpha -1>} \times\frac{\mathcal{R}[x]}{<x^\beta -1>}$, for some positive integers $\alpha$ and $\beta$. In this paper, we study the algebraic structure of ${\Bbb Z}_p\mathcal{R}$-additive cyclic codes of length $(\alpha, \beta)$. To do this, we determine their generator polynomials and minimal generating sets. Moreover, we discuss the duality of the ${\Bbb Z}_p\mathcal{R}$-additive cyclic codes and obtain their generator polynomials. We also study the structure of additive constacyclic codes and quantum codes over ${\Bbb Z}_p\mathcal{R}$.

Key Words: Additive cyclic codes, additive constacyclic codes, minimal generating set.

2010 Mathematics Subject Classification: Primary 12E20; Secondary 94B05, 94B15, 94B60.

Download the paper in pdf format here.