Two-dimensional Constacyclic Codes over $\mathbb{F}_q$

Autor:	Sagar, Vidya, Patel, Shikha, Garani, Shayan Srinivasa
Rok vydání:	2024
Předmět:	Computer Science - Information Theory
Druh dokumentu:	Working Paper
Popis:	We consider two-dimensional $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_{q}$ of area $M N$, where $q$ is some power of prime $p$ with $\gcd(M,p)=1$ and $\gcd(N,p)=1$. With the help of common zero (CZ) set, we characterize 2-D constacyclic codes. Further, we provide an algorithm to construct an ideal basis of these codes by using their essential common zero (ECZ) sets. We describe the dual of 2-D constacyclic codes. Finally, we provide an encoding scheme for generating 2-D constacyclic codes. We present an example to illustrate that 2-D constacyclic codes can have better minimum distance compared to their cyclic counterparts with the same code size and code rate. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.09915 Zobrazit plný text záznamu View this record from Arxiv