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On cycle-free lattices. (English) Zbl 1216.94039
Brualdi, Richard A. (ed.) et al., Combinatorics and graphs. Selected papers based on the presentations at the twentieth anniversary conference of IPM on combinatorics, Tehran, Iran, May 15–21, 2009. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4865-4/pbk). Contemporary Mathematics 531, 143-147 (2010).
Summary: It has been shown that high rate codes based on cycle-free Tanner graphs have minimum distance at most 2. So cycle-free Tanner graphs cannot support good codes. This result has been extended to a class of lattices based on a special construction. In this work, based on some new relationship which is derived between lattices and their corresponding label codes, we generalize those results to a larger class of lattices.
For the entire collection see [Zbl 1202.05003].
MSC:
94A24 Coding theorems (Shannon theory)
11H31 Lattice packing and covering (number-theoretic aspects)
05C38 Paths and cycles
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