Name
Title | ||
|---|---|---|
Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles |
Abstract | ||
|---|---|---|
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), $${\mathcal{W}(q)}$$ and $${\mathcal{H}(3,q^{2})}$$ . For $${\mathcal{W}(q)}$$ , and $${\mathcal{H}(3,q^{2})}$$ , we are able to describe small weight codewords geometrically. For $${\mathcal{Q}(4,q)}$$ , q odd, and for $${\mathcal{H}(4,q^{2})^{D}}$$ , we improve the best known lower bounds on the minimum distance, again only using geometric arguments. Similar results are also presented for the LDPC codes LU(3,q) given in [Kim, (2004) IEEE Trans. Inform. Theory, Vol. 50: 2378---2388] |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10623-006-9017-6 | Des. Codes Cryptography |
Keywords | Field | DocType |
LDPC code,Generalized quadrangle,Minimum distance,51E12,94B05 | Discrete mathematics,Parity bit,Combinatorics,Low-density parity-check code,Generalized quadrangle,Mathematics,Quadric,Parabola | Journal |
Volume | Issue | ISSN |
42 | 1 | 0925-1022 |
Citations | PageRank | References |
7 | 0.50 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jon-Lark Kim | 1 | 312 | 34.62 |
| Keith E. Mellinger | 2 | 86 | 13.04 |
| Leo Storme | 3 | 197 | 38.07 |