Enumeration of a class of sequences generated by inversions
Çeşmelioğlu, Ayça and Meidl, Wilfried and Topuzoğlu, Alev (2008) Enumeration of a class of sequences generated by inversions. In: 1st International Workshop on Coding and Cryptology, Fujian, China
Any permutation of a finite field F-q can be represented by a polynomial P-n(x) = (. . . ((a(0)x a(1))(q-2) + a(2))(q-2) ... a(n))(q-2) + a(n+1), for some n >= 0. In this note we present the number of distinct permutations of the types P-2(x) and P-3(x) with full cycle. These results extend earlier work on the inversive pseudorandom number generator and on P-1.
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