Hadamard's coding matrix and some decoding methods
Session
Computer Science and Communication Engineering
Description
In this paper, we will show a way to form Hadamard's code order n 2p (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 du,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
Bertan Karahoda
Session Co-Chair
Krenare Pireva
Proceedings Editor
Edmond Hajrizi
ISBN
978-9951-550-19-2
Location
Pristina, Kosovo
Start Date
10-2019 1:30 PM
End Date
10-2019 3:00 PM
DOI
10.33107/ubt-ic.2019.273
Recommended Citation
Leka, Hizer; Jusufi, Azir; and Kabashi, Faton, "Hadamard's coding matrix and some decoding methods" (2019). UBT International Conference. 273.
https://knowledgecenter.ubt-uni.net/conference/2019/events/273
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 2p (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 du,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.