New algebraic decoding of the quadratic residue codes


主讲人:张耀祖 台湾义守大学




内容介绍:Quadratic residues (QR) codes, introduced by Prange in 1958, are cyclic codes ?with code rates not less than 1/2 and generally have large minimum distances, so ?that most of the known QR codes are the best-known codes. Both the famous ?Hamming code of length 7 and the Golay codes are QR codes. However, it is ?difficult to decode QR codes, and except for those of low lengths, the decoders ?for QR codes appeared quite late. The first algebraic decoder of Golay code of ?length 23 was proposed by Elia in 1987. From 1990, Reed et al. published a ?series of papers about algebraic decoding of QR codes of lengths 31, 41, 47, and ?73. After that, the coding group of I-Shou University continued the QR decoding ?study and developed decoders of lengths 71, 79, 89, 97, 103, and 113. Hence, all ?binary QR codes of lengths not exceed 113 are decoded. In this presentation, we ?give a brief review of decoding QR codes. It also includes the most recent works ?done by I-Shou coding group which improve the decoding processes for the ?practical hardware implementation.