Explicit constructions of graphs without short cycles and low density codes


We give an explicit construction of regular graphs of degree 2r withn vertices and girth ≧c logn/logr. We use Cayley graphs of factor groups of free subgroups of the modular group. An application to low density codes is given.

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Margulis, G.A. Explicit constructions of graphs without short cycles and low density codes. Combinatorica 2, 71–78 (1982). https://doi.org/10.1007/BF02579283

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