A Deterministic Dimension Property of Twisted Goppa Codes
Information Theory
2025-11-18 v1 math.IT
Abstract
This paper presents a large-scale computational study on the dimensional properties of twisted Goppa codes. Through the systematic analysis of over 50,000 parameter sets, we uncover a remarkable deterministic regularity: the actual dimension k of a twisted Goppa code is uniquely determined by a set of macro-parameters (q,m,t,b,u). Specifically, when the order of the finite field q, the extension degree m, the degree t of the Goppa polynomial, the translation parameter b of the automorphism, and the order u of the transformation are fixed, the dimension k of the generated code remains constant.
Cite
@article{arxiv.2511.13601,
title = {A Deterministic Dimension Property of Twisted Goppa Codes},
author = {Kai Wang},
journal= {arXiv preprint arXiv:2511.13601},
year = {2025}
}
Comments
This is the first version (v1) of an original research article. 7 pages, containing 1 primary data table