LCD Codes and Quantum Mysteries: Insights into Construction Techniques from Cyclic Codes over Finite Commutative Rings

Abstract

Let  be a field of order q, whereas and are two not zero items of , and q is a fraction of an unusual prime p. This article's main objective is to investigate the structural characteristics of cyclic codes over the finite ring R = .  In . The researcher constructs quantum-error-correcting (QEC) codes over R by decomposing the ring R into its parts, , utilising orthogonal idempotent . As an example, we create a few ideal LCD codes.