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arXiv · 2503.14058

Strongly regular generalized partial geometries and associated LDPC codes

Lijun Ma·Changli Ma·Zihong Tian
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Abstract

In this paper, we introduce strongly regular generalized partial geometries of grade $r$, which generalise partial geometries and strongly regular $(\alpha,\beta)$-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.

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Lijun Ma, Changli Ma, Zihong Tian. 2025-03-18. Strongly regular generalized partial geometries and associated LDPC codes. https://arxiv.org/abs/2503.14058

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