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Link to original content: https://link.springer.com/doi/10.1007/BF02579283
Explicit constructions of graphs without short cycles and low density codes | Combinatorica Skip to main content
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Explicit constructions of graphs without short cycles and low density codes

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Abstract

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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References

  1. P. Erdős andH. Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl,Wiss. Z. Univ. Halle—Wittenberg, Math.-Nat. R. 12 (1963), 251–258.

    Google Scholar 

  2. R. G. Gallager,Low-density parity-check codes, M. I. T. Press, Cambridge, Mass. 1963.

    Google Scholar 

  3. K. C. Gunning,Lectures on modular forms, Ann. Math. Studies48, Princeton University Press, Princeton N. J. 1962.

    MATH  Google Scholar 

  4. M. Hall, Jr.,The theory of groups, Macmillan, N. Y. 1959.

  5. G. H. Hardy andE. M. Wright,An introduction to the theory of numbers, 5th ed., Clarendon Press, Oxford 1979.

    MATH  Google Scholar 

  6. I. Kra,Automorphic forms and Kleinian groups, Benjamin, Reading, Mass. 1972.

    MATH  Google Scholar 

  7. W. Magnus, A. Karrass andD. Solitar,Combinatorial group theory, Interscience, N. Y. 1966.

  8. H. Walther andH.-J. Voss,Über Kreise in Graphen, VEB Deutscher Verlag der Wiss., Berlin 1974.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Problems of Information Transmission, 19 Yermolovoi Str., 103051, Moscow, U.S.S.R.

    G. A. Margulis

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  1. G. A. Margulis
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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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  • DOI: https://doi.org/10.1007/BF02579283

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