Permutation Polynomial

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a permutation polynomial (for a given finite ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x mapsto g(x) is one-to-one. In case the ring is a finite field, they are (under certain assumptions) essentially Dickson polynomials which are closely related to the Chebyshev polynomials. In the case of finite rings Z/nZ, such polynomials have also been studied and applied in the interleaver component of error detection and correction algorithms. For the finite ring Z/nZ one can construct quadratic permutation polynomials. Actually it is possible if and only if n is divisible by p2 for some prime number p. The construction is surprisingly simple, nevertheless it can produce permutations with certain good properties. That is why it has been used in the interleaver component of turbo codes in 3GPP Long Term Evolution mobile telecommunication standard.