Keith E. Mellinger

Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles

We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in PG(4,q) to find information about the LDPC codes defined by Q (4,q),

2-dimensional optical orthogonal codes from singer groups

{\mathcal{W}(q)}

LDPC Codes from Triangle-Free Line Sets

and

Classes of optical orthogonal codes from arcs in root subspaces

{\mathcal{H}(3,q^{2})}

Constructions of Optical Orthogonal Codes from Finite Geometry

. For