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LDPC codes generated by conics in the classical projective plane

Abstract

We construct various classes of low-density parity-check codes using point-line incidence structures in the classical projective plane PG(2,q). Each incidence structure is based on the various classes of points and lines created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distance. Some arguments involve the geometry of two conics in the plane. As a result, we prove, under mild conditions, the existence of two conics, one entirely internal or external to the other. We conclude with some simulation data to exhibit the effectiveness of our codes.

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Correspondence to Keith E. Mellinger.

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Communicated by R. Hill

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Droms, S.V., Mellinger, K.E. & Meyer, C. LDPC codes generated by conics in the classical projective plane. Des Codes Crypt 40, 343–356 (2006). https://doi.org/10.1007/s10623-006-0022-6

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Keywords

  • LDPC code
  • Projective plane
  • Conic

AMS Classification

  • 51E22
  • 94B05