Systematic Non-Binary Extension of LDPC-CSS Codes Preserving Orthogonality

TL;DR

This paper introduces a systematic method to extend binary LDPC-CSS quantum error-correcting codes to non-binary finite fields while preserving their orthogonality and support properties, broadening their applicability.

Contribution

The authors propose a novel systematic construction for non-binary extensions of LDPC-CSS codes that maintain orthogonality and support, applicable beyond low-density cases.

Findings

Finite-field extensions preserve code support and orthogonality.

Method applicable to arbitrary CSS codes.

Facilitates broader quantum error correction applications.

Abstract

We study finite-field extensions that preserve the same support as the parity-check matrices defining a given binary CSS code. Here, an LDPC-CSS code refers to a CSS code whose parity-check matrices are orthogonal in the sense that each pair of corresponding rows overlaps in an even (possibly zero) number of positions, typically at most twice in sparse constructions. Beyond the low-density setting, we further propose a systematic construction method that extends to arbitrary CSS codes, providing feasible finite-field generalizations that maintain both the binary support and the orthogonality condition.