Families of sequences with good family complexity and cross-correlation measure
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In this paper we study pseudorandomness of a family of sequences in terms of two measures, the family complexity (f-complexity) and the cross-correlation measure of order ℓ. We consider sequences not only on binary alphabet but also on k-symbols (k-ary) alphabet. We first generalize some known methods on construction of the family of binary pseudorandom sequences. We prove a bound on the f-complexity of a large family of binary sequences of Legendre-symbols of certain irreducible polynomials. We show that this family as well as its dual family have both a large family complexity and a small cross-correlation measure up to a rather large order. Next, we present another family of binary sequences having high f-complexity and low cross-correlation measure. Then we extend the results to the family of sequences on k-symbols alphabet.
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