论文信息 - Explicit constructions of graphs without short cycles and low density codes

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.

G. A. Margulis | G. Margulis

[1] Michael Horstein,et al. Review of 'Low-Density Parity-Check Codes' (Gallager, R. G.; 1963) , 1964, IEEE Transactions on Information Theory.

[2] Heinz-Jürgen Voss,et al. Über Kreise in Graphen , 1974 .

[3] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .

[4] J. Lehner,et al. Lectures on modular forms , 1962 .

[5] Robert C. Gunning,et al. Lectures on Modular Forms. (AM-48) , 1962 .

[6] Robert G. Gallager,et al. Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[7] Irwin Kra,et al. Automorphic Forms And Kleinian Groups , 1972 .