Strongly regular generalized partial geometries and associated LDPC codes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866917959513931776 |
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| author | Ma, Lijun Ma, Changli Tian, Zihong |
| author_facet | Ma, Lijun Ma, Changli Tian, Zihong |
| contents | In this paper, we introduce strongly regular generalized partial geometries of grade $r$, which generalise partial geometries and strongly regular $(α,β)$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strongly regular generalized partial geometries and associated LDPC codes Ma, Lijun Ma, Changli Tian, Zihong Combinatorics In this paper, we introduce strongly regular generalized partial geometries of grade $r$, which generalise partial geometries and strongly regular $(α,β)$-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. |
| title | Strongly regular generalized partial geometries and associated LDPC codes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.14058 |