On QC and GQC algebraic geometry codes
Information Theory
2026-02-06 v1 Algebraic Geometry
math.IT
Abstract
We present new constructions of quasi-cyclic (QC) and generalized quasi-cyclic (GQC) codes from algebraic curves. Unlike previous approaches based on elliptic curves, our method applies to curves that are Kummer extensions of the rational function field, including hyperelliptic, norm-trace, and Hermitian curves. This allows QC codes with flexible co-index. Explicit parameter formulas are derived using known automorphism-group classifications.
Cite
@article{arxiv.2602.05097,
title = {On QC and GQC algebraic geometry codes},
author = {Matteo Bonini and Arianna Dionigi and Francesco Ghiandoni},
journal= {arXiv preprint arXiv:2602.05097},
year = {2026}
}