CS 681: Computational Number Theory and Algebra Lecture 2: Reed Solomon code Summary: CS 681: Computational Number Theory and Algebra Lecture 2: Reed Solomon code Lecturer: Manindra Agrawal Notes by: Anindya De August 8, 2006. 1 Reed Solomon codes-Encoding Let b0, b1, . . . , bn be a binary sequence which is to be coded for handling a maximum of t errors. Fix a k < n and split b0, b1, . . . , bn into n/k blocks of k bits each. Let these be c0, c1, . . . ck. View each ci as an element in F2k . Define P(x) = n/k-1 i=1 cixi. Let dj = P(ej) for e0, e1, e2, . . . , em-1 F2k . We will output d0, d1, d2, . . . , dm-1 as the encoded message. The input size is n bits as compared to the output size which is mk bits. Also we assume that the number of errors is atmost t i.e. atmost t out of the m di get corrupted. Note that though theoretically it can correct only upto t errors, the number of errors it can correct in practice is much larger. This is because we assume that the t bits that get corrupted are in t different di's but usually errors occur in blocks. Hence it can correct upto tk errors. 2 Decoding Collections: Computer Technologies and Information Sciences