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Cyclic code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. ==Definition== Let be a linear code over a finite field of block length ''n''. is called a cyclic code if, for every codeword ''c''=(''c''1,...,''c''n) from ''C'', the word (''c''n,''c''1,...,''c''n-1) in obtained by a cyclic right shift of components is again a codeword. Because one cyclic right shift is equal to ''n'' − 1 cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore the linear code is cyclic precisely when it is invariant under all cyclic shifts. Cyclic Codes have some additional structural constraint on the codes. They are based on Galois fields and because of their structural properties they are very useful for error controls. Their structure is strongly related to Galois fields because of which the encoding and decoding algorithms for cyclic codes are computationally efficient.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Cyclic code」の詳細全文を読む
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