Quasi-cyclic NMDS codes

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• 作者：Hongxi Tong ; Ding Yang
• 关键词：94B05 ; 94B15 ; 14H05 ; 14H37 ; 14H52
• 刊名：Finite Fields and Their Applications
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：24
• 期：Complete
• 页码：45-54
• 全文大小：194 K

文摘

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.