Abstract
In this paper we concern ourself with the question, whether there exists a fix-free code for a given sequence of codeword lengths. We focus mostly on results which shows the $\frac{3 }{ 4}$-conjecture for special kinds of lengths sequences.
Highlights
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In this paper we concern ourself with the question, whether there exists a fix-free code for a given sequence of codeword lengths
For the proof of the theorem and its generalization, we introduce π-systems, which are special kinds of fix-free codes with
Summary
-conjecture for special kinds of lengths sequences. -Conjecture theorem was first shown by Kukorelly and Zeger in (10) for the binary case. -Conjecture theorem was first shown by Kukorelly and Zeger in (10) for the binary case. We generalize this theorem to q-ary alphabets. For the proof of the theorem and its generalization, we introduce π-systems, which are special kinds of fix-free codes with. We give a generalization of a theorem from Kukorelly and Zeger (10), which was shown for the binary case originally. We give a generalization of a theorem of Yekhanin (8), which shows that for binary codes if the Kraftsum of the first level which occurs in the code together with it neighboring level is bigger than. ∆nB(C) := ∆nP (C) ∪ ∆nS(C) ⊆ An. For proving the theorem, Yekhanin introduced in (8) a special kind of fix-free codes, which he called π-systems: Definition 1 Let |A| = 2, we say D ⊆
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