Hadamard's Coding Matrix and Some Decoding Methods

EasyChair Preprint no. 3218

10 pagesDate: April 22, 2020

Abstract

In this paper, we will show a way to form Hadamard's code order n=2^p (where p is a positive integer) with the help of Rademacher functions, through which matrix elements are generated whose binary numbers {0,1} , while its columns are Hadamard's encodings and are called Hadamard's coding matrix. Two illustrative examples will be taken to illustrate this way of forming the coding matrix. Then, in a graphical manner and by means of Hadamard's form codes, the message sequence encoding as the order coding matrix will be shown. It will also give Hadamard two methods of decoding messages, which are based on the so-called Haming distance. Haming's distance between two vectors u and v was denoted by d(u,v) and represents the number of places in which they differ. In the end, three conclusions will be given, where a comparison will be made of encoding and decoding messages through Haming's coding matrices and distances.

Keyphrases: decoding, encoding, Hadamard matrix, Hadamard’s code codeword, Hamming distance, Rademacher function