Session

Management, Business and Economics

Description

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.

Keywords:

Hadamard Matrix, Hadamard’s code, Codeword, Encoding, Decoding, Rademacher Function, Hamming distance.

Session Chair

Hasan Metin

Session Co-Chair

Leonita Braha Vokshi

Proceedings Editor

Edmond Hajrizi

ISBN

978-9951-550-19-2

First Page

37

Last Page

44

Location

Pristina, Kosovo

Start Date

26-10-2019 3:30 PM

End Date

26-10-2019 5:00 PM

DOI

10.33107/ubt-ic.2019.364

Included in

Business Commons

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Oct 26th, 3:30 PM Oct 26th, 5:00 PM

Hadamard's Coding Matrix and Some Decoding Methods

Pristina, Kosovo

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.