On a class of twisted elliptic curve codes
Information Theory
2026-05-11 v3 math.IT
Abstract
Motivated by the studies of twisted generalized Reed-Solomon (TGRS) codes, we initiate the study of twisted elliptic curve codes (TECCs) in this paper. In particular, we study a class of TECCs with one twist. The parity-check matrices of the TECCs are explicitly given by computing the Weil differentials. Then the sufficient and necessary conditions of self-duality are presented. The minimum distances of the TECCs are also determined. Moreover, examples of MDS, AMDS, self-dual and MDS self-dual TECCs are given. Finally, we calculate the dimensions of the Schur squares of TECCs and show the non-equivalence between TECCs and ECCs/GRS codes.
Keywords
Cite
@article{arxiv.2509.03034,
title = {On a class of twisted elliptic curve codes},
author = {Xiaofeng Liu and Jun Zhang and Fang-Wei Fu},
journal= {arXiv preprint arXiv:2509.03034},
year = {2026}
}