Large Families of Pseudorandom Sequences of k Symbols and Their Complexity – Part II

  • R. Ahlswede
  • C. Mauduit
  • A. Sárközy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


We continue the investigation of Part I, keep its terminology, and also continue the numbering of sections, equations, theorems etc.

Consequently we start here with Section 6. As mentioned in Section 4 we present now criteria for a triple (r,t,p) to be k–admissible. Then we consider the f–complexity (extended now to k–ary alphabets) \(\Gamma_k(\mathcal{F})\) of a family \(\mathcal{F}\). It serves again as a performance parameter of key spaces in cryptography. We give a lower bound for the f–complexity for a family of the type constructed in Part I. In the last sections we explain what can be said about the theoretically best families \(\mathcal{F}\) with respect to their f–complexity \(\Gamma_k(\mathcal{F})\). We begin with straightforward extensions of the results of [4] for k=2 to general k by using the same Covering Lemma as in [1].


Binary Sequence Prime Divisor Pseudorandom Sequence Irreducible Polynomial Acta Arith 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • C. Mauduit
    • 2
  • A. Sárközy
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2. 

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