Back to Search
Start Over
On the structure of $1$-generator quasi-polycyclic codes over finite chain rings
- Publication Year :
- 2021
-
Abstract
- Quasi-polycyclic (QP for short) codes over a finite chain ring $R$ are a generalization of quasi-cyclic codes, and these codes can be viewed as an $R[x]$-submodule of $\mathcal{R}_m^{\ell}$, where $\mathcal{R}_m:= R[x]/\langle f\rangle$, and $f$ is a monic polynomial of degree $m$ over $R$. If $f$ factors uniquely into monic and coprime basic irreducibles, then their algebraic structure allow us to characterize the generator polynomials and the minimal generating sets of 1-generator QP codes as $R$-modules. In addition, we also determine the parity check polynomials for these codes by using the strong Gr\"{o}bner bases. In particular, via Magma system, some quaternary codes with new parameters are derived from these 1-generator QP codes.
- Subjects :
- Computer Science - Information Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.04914
- Document Type :
- Working Paper