Strongly regular generalized partial geometries and associated LDPC codes

Abstract

In this paper, we introduce strongly regular generalized partial geometries of grade $r$, which generalise partial geometries and strongly regular $(\hat{I}\pm ,{\hat{I}}^2)$-geometries. By the properties of quadrics in PG$(2,q)$ and PG$(3,q)$, we construct two classes of strongly regular generalized partial geometries of grade $3$. Besides, we define low-density parity-check (LDPC) codes by considering the combinatorial structures of strongly regular generalized partial geometries and derive bounds on minimum distance, dimension and girth for the LDPC codes.