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Proposition 4: Let a be a q-ary finite-field sequence of period P a and let N be a positive integer such that 1 N Pa 0 1: Let the minimum polynomial of a be an irreducible polynomial of degree n: Then the linear complexities of a and a (N) are equal if any of the two following conditions is satisfied. 1) q = 2 and n is a prime. 2) P a = q n 0 1 and N = q m… (More)

In the last century, Desire Andre obtained many remarkable properties of the numbers of alternating permutations, linking them to trigonometric functions among other things. By considering the probability that a random permutation is alternating and that a random sequence (from a uniform distribution) is alternating, and by conditioning on the first element… (More)

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