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
Famous quotes containing the word definition:
“Perhaps the best definition of progress would be the continuing efforts of men and women to narrow the gap between the convenience of the powers that be and the unwritten charter.”
—Nadine Gordimer (b. 1923)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)