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Unformatted text preview: 1.Introduction: Cyclic codes form an important subclass of linear codes. These codes are attractive for two reasons: first, encoding and decoding can be implemented easily by employing shiftregisters with feedback connections (as will be seen later); and second, because they have considerable inherent algebric structure, it is possible to find various practical methods for decoding them. In this section the reader can find a general overview of binary cyclic codes followed by their mathematical representation and their main algebric properties (section 2); The third section deals with the encoding procedure and finally, the structure of the generator and paritycheck matrices will be shown. In order to fully understand the cyclic codes material, it is advised to comprehend thoroughly the linear block codes issue first. 2.Description of cyclic codes: 2.1 Cyclic code definition: Lets start with the definition of cyclic shift : If the components of an ntuple are cyclically shifted one place to the right, we obtain another ntuple: which is called a cyclic shift of . If the components of are cyclically shifted i places to the right, the resultant ntuple would be : . Clearly, cyclically shifting i places to the right is equivalent to cyclically shifting ni places to the left. Cyclic code definition: An (n,k) linear code C is called a cyclic code if every cyclic shift of a code vector in C is also a code vector in C. 2.2 Polynomial representation: In order to develop the algebric properties of a cyclic code, we treat the components of a code vector as the coefficients of a polynomial as follows: . Thus, each code vector corresponds to a polynomial of degree n1 or less. We shall call the code polynomial of . Before looking further into cyclic codes, we'll go over some polynomial basics first:...
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 Spring '09
 profnaganagi
 Coding theory, Linear code, Cyclic code

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