We study some sufficient conditions of code- word lengths for theexistence of a fix-free code. Ahlswede et al. proposed the 3/4conjecture that formula(ell.) ≤3/4 implies the existence of afix-free code with lengths l_i when a = 2 i.e. the alphabet isbinary. We propose a more general conjecture, and prove that theupper bound of our conjecture is not greater than 3/4 for any finitealphabet. Moreover, we show that for any a≥2 our conjecture is trueif codeword lengths l_1,l_2...consist of only two kinds of lengths.
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