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.

翻译：受扭曲广义Reed-Solomon（TGRS）码研究的启发，本文首次系统性地探讨了扭曲椭圆曲线码（TECCs）。特别地，我们重点研究了一类具有单一扭曲的TECCs。通过计算Weil微分，我们明确给出了TECCs的奇偶校验矩阵。随后，我们提出了自对偶性的充分必要条件，并确定了TECCs的最小距离。此外，我们还给出了MDS、AMDS、自对偶及MDS自对偶TECCs的具体实例。最后，我们计算了TECCs的Schur平方的维数，并证明了TECCs与ECCs/GRS码之间的非等价性。