One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

Autor: Khormaei, Marziyeh Beygi, Nikseresht, Ashkan, Namazi, Shohreh
Rok vydání: 2022
Předmět:
Druh dokumentu: Working Paper
Popis: In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F=\mathbb{F}_q$. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual. Moreover, we prove that if there exists an asymptotically good family of one-sided repeated-root two-dimensional cyclic or constacyclic codes, then there exists an asymptotically good family of simple root two-dimensional cyclic or constacyclic codes with parameters at least as good as the first family. Furthermore, we show that several of the main results of the papers Rajabi and Khashyarmanesh (2018) and Sepasdar and Khashyarmanesh (2016) are not accurate and find other conditions needed for them to hold.
Databáze: arXiv