On a class of twisted elliptic curve codes
This work extends the concept of twisted codes to elliptic curves, offering new constructions for coding theorists interested in MDS and self-dual codes.
The paper introduces twisted elliptic curve codes (TECCs), a new class of error-correcting codes, and provides explicit parity-check matrices, self-duality conditions, and minimum distances. Examples of MDS, AMDS, and self-dual TECCs are given, and it is shown that TECCs are not equivalent to elliptic curve codes or GRS codes.
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.