Incidence structures from the blown up plane and LDPC codes

Improving the Rao-Nam secret key cryptosystem using regular EDF-QC-LDPC codes

This paper proposes an efficient joint secret key encryption-channel coding cryptosystem, based on regular Extended Difference Family Quasi-Cyclic Low-Density Parity-Check codes. The key length of the proposed cryptosystem decreases up to 85 percent using a new efficient compression algorithm. Cryptanalytic methods show that the improved cryptosystem has a significant security advantage over Ra...

LDPC codes generated by conics in the classical projective plane

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 point classes (internal, external) and line classes (skew, tangent, secant) created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distan...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

On LDPC Codes from (0, 1) -Geometries Induced by Finite Inversive Spaces of Even Order

Low Density Parity Check (LDPC) codes have enjoyed increasing interest during recent years. In general these are described in the terminology of sparse bipartite graphs containing no 4 -cycles, but an alternative way to deal with them are a particular class of incidence structures, namely partial linear spaces. This paper shows how to obtain a large class of partial linear spaces from inversive...

High-rate LDPC codes from unital designs

This paper presents a construction of very high-rate low-density parity-check (LDPC) codes based on the incidence matrices of unital designs. Like the projective geometry and oval designs, unital designs exist with incidence matrices which are significantly rank deficient. Thus high-rate LDPC codes with a large number of linearly dependent parity-check equations can be constructed. The LDPC cod...