Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes
Document Type
Article
Publication Date
1-1-2024
Abstract
Let s >= 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(alpha(1), alpha(2), ... , alpha(s)), where alpha(i) is an element of F-q\textbackslash{0}, 1 <= i <= s, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing F-q reversibility. The aim to introduce the F-q reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases (A, T, G, C).
Keywords
cyclic code, quantum code, Gray map, non-chain ring, DNA code, DNA reversibility
Divisions
MathematicalSciences
Funders
Princess Nourah bint Abdulrahman University (PNU) , Riyadh, Saudi Arabia under Researchers Supporting Project (PNURSP2024R231),Institute of Mathematical Sciences (IMS) , University of Malaya (UM) , Malaysia
Publication Title
AIMS Mathematics
Volume
9
Issue
3
Publisher
AIMS Press
Publisher Location
PO BOX 2604, SPRINGFIELD, MO 65801-2604, UNITED STATES