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Constructing effectively MDS and recursive MDS matrices by Reed-Solomon codes

CSKH-02.2016 - (Tóm tắt) - Mã khả tách có khoảng cách cực đại (mã MDS) đã được nghiên cứu rộng rãi trong lý thuyết mã sửa sai. Hiện nay, mã MDS đang được quan tâm và ứng dụng trong mật mã. Nhiều phương pháp khác nhau đã được nghiên cứu để xây dựng các ma trận MDS. Trong đó, phương pháp xây dựng các ma trận MDS từ mã MDS là một phương pháp được sử dụng phổ biến. Bài báo này trình bày các phương pháp xây dựng hiệu quả các ma trận MDS/MDS truy hồi từ mã Reed-Solomon (RS). Các ma trận MDS/MDS truy hồi được sinh ra từ các mã này đạt hiệu quả cao trong các ứng dụng mật mã.

Abstract- Maximum Distance Separable (MDS) codes have been studied widely in coding theory. Recently, MDS codes have been applied in cryptography. Many different methods have been proposed for finding MDS matrices. Among these methods, the method for constructing them from MDS codes is a common one. In this paper, some methods for constructing effectively MDS and recursive MDS matrices from Reed-Solomon (RS) codes are presented. The MDS and recursive MDS matrices generated from these codes are useful and efficient for cryptographic applications.

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