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，本文首次提出对扭曲椭圆曲线码（TECC）的研究。具体而言，我们研究了一类具有单扭曲的TECC。通过计算Weil微分，显式给出了TECC的校验矩阵。进而给出了自对偶性的充分必要条件，并确定了TECC的最小距离。此外，给出了MDS、AMDS、自对偶及MDS自对偶TECC的实例。最后，计算了TECC的Schur平方的维数，并证明了TECC与ECC/GRS码之间的非等价性。