Raziyeh Molaei, Kazem Khashyarmanesh: ${\Bbb Z}_{p^r} {\Bbb Z}_{p^s}$-Double cyclic codes, 177-198

Abstract:

Let $p$ be a prime number and $r, s$ be positive integers such that $r \le s$. This paper is concerned with $\mathbb{Z}_{p^r}\mathbb{Z}_{p^s}$-double cyclic codes. These codes can be identified as submodules of the ring

$$\mathbb{Z}_{p^r}/<x^\alpha-1> \times \mathbb{Z}_{p^r}/<x^\beta-1> \times \mathbb{Z}_{p^s}/<x^\gamma-1> \times \mathbb{Z}_{p^s}/<x^\eta-1>,$$

where $\alpha, \beta, \gamma$ and $\eta$ are positive integers. We determine the generator polynomials and minimal generating sets for this family of codes. Furthermore, we classify $\mathbb{Z}_p\mathbb{Z}_{p^2}$-double cyclic codes.

Key Words: Double cyclic codes, generator polynomials, minimum generating sets, dual code.

2020 Mathematics Subject Classification: Primary 12E20, 94B05, 94B15; Secondary 94B60.

Download the paper in pdf format here.