Sufficient Conditions for Existence of Binary Fix-Free Codes
نویسندگان
چکیده
منابع مشابه
-Conjecture for Fix-Free Codes
A fix-free code is a code, which is prefix-free and suffix-free, i.e. any codeword of a fix-free code is neither a prefix, nor a suffix of another codeword. Fix-free codes were first introduced by Schützenberg (4) and Gilbert and Moore (5), where they were called never-self-synchronizing codes. Ahlswede, Balkenhol and Khachatrian propose in (6) the conjecture that a Kraftsum of a lengths sequen...
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Two sufficient conditions are given for the existence of binary fix-free codes. The results move closer to the Ahlswede-Balkenhol-Khachatrian conjecture that Kraft sums of at most 3=4 suffice for the existence of fix-free codes. For each nonnegative integer n let f0; 1gn denote the set of all binary words of length n, and let f0; 1g denote the set of all finite length binary words, including th...
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Two sufficient conditions are given for the existence of binary fix-free codes. The results move closer to the Ahlswede-Balkenhol-Khachatrian conjecture that Kraft sums of at most suffice for the existence of fix-free codes. For each nonnegative integer let denote the set of all binary words of length , and let denote the set of all finite length binary words, including the empty word. A binary...
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Contents 1 The Kraftinequality for fix-free codes 13
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Proof Let C be a (n, k, d)q code. Then it has q k codewords of length n. Project C to a k − 1 dimensional space by only considering the first k− 1 entries of each code words (see Figure 1). There are at most qk−1 possible strings of length k − 1 in Fk−1 q . However, we have in total qk code words so there must exist at least two codewords with the same projections. Thus the distance between the...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2005
ISSN: 0018-9448
DOI: 10.1109/tit.2005.855581