Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Hadamard code, named after Jacques Hadamard, is a system used for signal error detection and correction. It is one of the family of [2n, n + 1, 2n ¿ 1] codes. Especially for large n it has a poor rate but it is capable of correcting many errors. Hadamard codes can be considered ...Pilns apraksts
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Hadamard code, named after Jacques Hadamard, is a system used for signal error detection and correction. It is one of the family of [2n, n + 1, 2n ¿ 1] codes. Especially for large n it has a poor rate but it is capable of correcting many errors. Hadamard codes can be considered as a special case of Reed-Muller codes. In particular, first order Reed-Muller code are equivalent to Hadamard codes.The code is based on Hadamard matrices. If H is a Hadamard matrix of order 2n the codewords are constructed by taking the rows of H and ¿H as codewords, where each ¿1 is replaced by 0. In this way 2n + 1 code words are constructed that each have a length of 2n. Since the rows of a Hadamard matrix are orthogonal the minimum distance is 2n - 1. In this way a [2n, n + 1, 2n ¿ 1] code is constructed.