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On a class of twisted elliptic curve codes
[Submitted on 3 Sep 2025 (v1), last revised 22 Jul 2026 (this ve · 2025-09-03 · via cs.IT updates on arXiv.org

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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.

Submission history

From: Xiaofeng Liu [view email]
[v1] Wed, 3 Sep 2025 05:50:23 UTC (30 KB)
[v2] Tue, 25 Nov 2025 07:23:23 UTC (30 KB)
[v3] Fri, 8 May 2026 11:55:59 UTC (30 KB)
[v4] Tue, 23 Jun 2026 06:02:29 UTC (28 KB)
[v5] Wed, 22 Jul 2026 16:38:53 UTC (29 KB)