Algebraic Decoding of Quadratic Residue Codes Using Berlekamp-Massey Algorithm

陳延華(Yan-Haw Chen) ； 張肇健(Trieu-Kien Truong) ； 張耀祖(Yao-Tsu Chang) ； 李崇道(C. D. Lee) ； 陳璽煌(Shi-Huang Chen)

《Journal of Information Science and Engineering》 23卷1期 (2007/01) Pp. 127-145

https://doi.org/10.6688/JISE.2007.23.1.7

並列摘要

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey algorithm. By a modification of the technique developed by He et al., one can express the unknown syndromes as functions of the known syndromes. The unknown syndromes are determined by an efficient algorithm also developed in this paper. With the appearance of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the Berlekamp-Massey algorithm. The decoding scheme, developed here, is easier to implement than the previous decoding algorithm developed for the Golay code and the (47, 24, 11) QR code. Moreover, it can be extended to decode all codes of the family of binary quadratic residue codes with irreducible generating polynomials.

並列關鍵字

quadratic residue codes ； unknown syndromes ； known syndromes ； Berlekamp-Massey algorithm ； error-locator polynomial