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Synopsis
Binary Codes are studied in information theory, electrical engineering, mathematics and computer science. They are used to design efficient and reliable data transmission methods. Linear codes are easier to deal with compared to nonlinear codes. Certain nonlinear binary codes though contain more codewords than any known linear codes with the same length and minimum distance. These include the Nordstrom-Robinson code, Kerdock, Preparata and Goethals codes. The Kerdock and Preparata codes are formal duals. It was not clear if these codes are duals in some more algebraic sense. Then, It was shown that when the Kerdock and Preparata codes are properly defined, they can be simply constructed as binary images under the Gray map of dual quaternary codes. Decoding codes mentioned is greatly simplified by working in the Z_4-domain, where they are linear. Observing Quaternary codes might lead to better binary codes. Here we define a class of quaternary codes, C(C_1,C_2) giving rise to a fixed pair of binary codes C_1= X (mod 2) and C_2= even words in X mapped coordinatewise to the Z_2 domain for X in C(C_1,C_2). We describe this class using the fixed pair of binary codes {C_1,C_2}.
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About the Author
Fatma Salim Al Kharousi, PhD. did BSc in Math at Sultan Qaboos University (SQU) , Oman. MSc in pure Math at Michigan State University, USA. PhD in Coding Theory at Queen Mary, University of London. Currently an assistant professor at SQU. Experienced in teaching math courses like Calculus, Linear Algebra and Discrete Math.
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- PublisherLAP LAMBERT Academic Publishing
- Publication date2013
- ISBN 10 3659427268
- ISBN 13 9783659427268
- BindingPaperback
- LanguageEnglish
- Number of pages168
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Describing Quaternary Codes Using Binary Codes
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ISBN 10: 3659427268
ISBN 13: 9783659427268
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Binary Codes are studied in information theory, electrical engineering, mathematics and computer science. They are used to design efficient and reliable data transmission methods. Linear codes are easier to deal with compared to nonlinear codes. Certain nonlinear binary codes though contain more codewords than any known linear codes with the same length and minimum distance. These include the Nordstrom-Robinson code, Kerdock, Preparata and Goethals codes. The Kerdock and Preparata codes are formal duals. It was not clear if these codes are duals in some more algebraic sense. Then, It was shown that when the Kerdock and Preparata codes are properly defined, they can be simply constructed as binary images under the Gray map of dual quaternary codes. Decoding codes mentioned is greatly simplified by working in the Z_4-domain, where they are linear. Observing Quaternary codes might lead to better binary codes. Here we define a class of quaternary codes, C(C_1,C_2) giving rise to a fixed pair of binary codes C_1= X (mod 2) and C_2= even words in X mapped coordinatewise to the Z_2 domain for X in C(C_1,C_2). We describe this class using the fixed pair of binary codes {C_1,C_2}. 168 pp. Englisch. Seller Inventory # 9783659427268
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Describing Quaternary Codes Using Binary Codes : Basics, Theory, Analysis
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LAP LAMBERT Academic Publishing, 2013
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ISBN 13: 9783659427268
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Binary Codes are studied in information theory, electrical engineering, mathematics and computer science. They are used to design efficient and reliable data transmission methods. Linear codes are easier to deal with compared to nonlinear codes. Certain nonlinear binary codes though contain more codewords than any known linear codes with the same length and minimum distance. These include the Nordstrom-Robinson code, Kerdock, Preparata and Goethals codes. The Kerdock and Preparata codes are formal duals. It was not clear if these codes are duals in some more algebraic sense. Then, It was shown that when the Kerdock and Preparata codes are properly defined, they can be simply constructed as binary images under the Gray map of dual quaternary codes. Decoding codes mentioned is greatly simplified by working in the Z_4-domain, where they are linear. Observing Quaternary codes might lead to better binary codes. Here we define a class of quaternary codes, C(C_1,C_2) giving rise to a fixed pair of binary codes C_1= X (mod 2) and C_2= even words in X mapped coordinatewise to the Z_2 domain for X in C(C_1,C_2). We describe this class using the fixed pair of binary codes {C_1,C_2}. Seller Inventory # 9783659427268
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Describing Quaternary Codes Using Binary Codes
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ISBN 13: 9783659427268
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Al Kharousi Fatma SalimFatma Salim Al Kharousi, PhD. did BSc in Math at Sultan Qaboos University (SQU) , Oman. MSc in pure Math at Michigan State University, USA. PhD in Coding Theory at Queen Mary, University of London. Currently a. Seller Inventory # 5155584
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