Definition
Let be a linear code over a finite field of block length n. is called a cyclic code, if for every codeword c=(c1,...,cn) from C, the word (cn,c1,...,cn-1) in obtained by a cyclic right shift of components is again a codeword. Same goes for left shifts. One right shift is equal to n − 1 left shifts and vice versa. 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.
Read more about this topic: Cyclic Code
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