eSeminar: Construction of Quantum Codes using Constacyclic Codes

There are several convenient ways to construct quantum codes from classical codes, the CSS and Hermitian construction are two popular among them. Here, we describe how classical (particularly, constacyclic) codes have been successfully producing new and better quantum codes under these constructions. First, we implement the idea over finite fields and then extend to non-commutative rings followed by commutative rings. From an application point of view, many quantum codes outperforming the best-known codes are constructed.