Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582966 | Finite Fields and Their Applications | 2013 | 10 Pages |
Abstract
Quasi-cyclic (QC) codes constitute a remarkable generalization of cyclic codes, and near-MDS (NMDS) codes are a family of codes obtained by weakening the restrictions of MDS codes. In this paper, we consider the QC NMDS codes by combining these two concepts. By choosing some elliptic curves with many rational points, we give a construction of QC NMDS codes based on the action of an elliptic curve automorphism on the rational points of the curve. Moreover, we calculate explicit example over finite fields of characteristic 2, 3, 5 or 7.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Hongxi Tong, Yang Ding,