- All Journals
- Al-Qadisiyah University
- Basrah University
- Kirkuk University
- Mosul University
- The Iraqi Borad for Medical Specialization
- University of Anbar
- University of Technology
- Al Mustafa University
- Al-Zahraa University for Women
- Alnoor University
- Kunooz University
- Misan University
- Ninevah University
- Tikrit University
- University of Al-Hamdaniya
- University of Kerbala
On representation of Hadamard Codes | ||
| Al-Fatih journal | ||
| Article 1, Volume 4, Issue 32, 2008, Pages 102-109 | ||
| Authors | ||
| Khalid H. Hameed; Hameed k. Dawiod | ||
| Abstract | ||
| Hadamard matrices (codes) were defined by the French mathematician M.J.Hadamard in 1893,[Hadamard," Resolution d’une question relative aux dêterminants" ,pp . 240-246,(1893)], called now Hadamard matrices.Hadamard matrix is a square array of +1,-1 whose rows and columns are mutually orthogonal.If the first row and first column contain only +1 ,the matrix is said to be in normal form.We can replace “+1” with “0” and “-1” with “1” to express Hadamard matrix using the logic elements {0,1}.Since, Hadamard codes are orthogonal and belong to class of linear codes,they are used in error correcting codes.Error correcting codes (E.C.C)which are very useful in sending information over long distances or through channels where errors might occur in the message. Hadamard code was used by B.j.Falkowski and T.Sasao, [ Falkowski and Sasao, “Unified algorithm to generate Walash functions in four different orderings and its programmable hardware implementations”,p.822,2005], to generate Walsh functions.Walsh functions were invented in 1923 by the American mathematician J.L.Walsh (1895-1973) ,see,[ Walsh, “Aclosed set of normal orthogonal functions”,pp.5-24,(1923)]. Walsh functions are used in image processing, see [Yaroslavsky,”Digital holography and digital image processing: principle,methods,algorithms”,p.50]. | ||
|
Statistics Article View: 185 PDF Download: 43 |
||