Some New Optimal Skew Cyclic Codes With Derivation
Year: 2025
Type: article
Abstract: Our study included a class of cyclic codes named δα,ζ−cyclic codes over the ringR= F2m+uF2m+u2F2m, wheremis an odd positive integer withu3= 1. These codes are modules over the ringR[x, α, δα,ζ] with automorphism α and α-derivation δα,ζ(where ζ ∈R). The structure of ringR[x, α, δα,ζ] is presented to develop linear codes over the ring. The center of the ring is characterized for all inner α-derivations δα,ζwhere ζ is taken as an arbitrary element of the ring fixed by α. In addition, an algorithm was developed and implemented in MAGMA to perform division in this ring. The generator and parity-check matrices for δα,ζ−cyclic codes are proposed, and examples of new optimal δα,ζ−cyclic codes with better minimum Hamming distance than those already existing in the Markus Grassl code tables are provided.
Source: IEEE Access
Authors: Asia Noor, Atif Hasan Soori, Muhammad Shoaib Arif, Kamaleldin Abodayeh
Institutions: Air University, Prince Sultan University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,075
Funder: Prince Sultan University
OpenAlex ID: W4411599671