Constructing CSS-T Codes from Extended Quasi-Cyclic Codes

Abstract

We analyze a construction of quasi-cyclic codes in an extension field based on the polynomials which generate the corresponding codes in the base fields. We establish a set of code operations on which trace relationships between extended quasi-cyclic codes are the same as the operations taken on the original codes. We also discuss how these relationships can be used to construct CSS-T codes for quantum-error correction.