English

On the dimensions of certain LDPC codes based on q-regular bipartite graphs

Information Theory 2007-12-04 v3 Discrete Mathematics math.IT

Abstract

An explicit construction of a family of binary LDPC codes called LU(3,q), where q is a power of a prime, was recently given. A conjecture was made for the dimensions of these codes when q is odd. The conjecture is proved in this note. The proof involves the geometry of a 4-dimensional symplectic vector space and the action of the symplectic group and its subgroups.

Keywords

Cite

@article{arxiv.cs/0506011,
  title  = {On the dimensions of certain LDPC codes based on q-regular bipartite graphs},
  author = {Peter Sin and Qing Xiang},
  journal= {arXiv preprint arXiv:cs/0506011},
  year   = {2007}
}

Comments

3 pages corrected typos: in inequality (2) changed a minus sign to plus v3.corrected 2 typos in Lemma 3.5 and added Journal-ref

R2 v1 2026-07-22T12:23:41.005Z