Characterization of Nearly Self-Orthogonal Quasi-Twisted Codes and Related Quantum Codes

TL;DR

This paper explores nearly self-orthogonal quasi-twisted codes for quantum error correction, expanding inner product choices and establishing new bounds, resulting in record-breaking quantum codes.

Contribution

It introduces a broader framework for constructing quantum codes using quasi-twisted codes with various inner products, and provides improved minimum distance bounds.

Findings

Expanded inner product options for code construction

Refined lower bounds on quantum code minimum distance

Numerous record-breaking quantum codes discovered

Abstract

Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices of the inner product to also cover the symplectic and trace-symplectic inner products, in addition to the original Hermitian one. A refined lower bound on the minimum distance of the resulting quantum codes is established and illustrated. We report numerous record breaking quantum codes from our randomized search for inclusion in the updated online database.