Abstract
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].
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Ahlswede, R., Mauduit, C., Sárközy, A. (2006). Large Families of Pseudorandom Sequences of k Symbols and Their Complexity – Part II. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_17
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DOI: https://doi.org/10.1007/11889342_17
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