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

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.