On the dimensions of certain LDPC codes based on q-regular bipartite graphs
<|reference_start|>On the dimensions of certain LDPC codes based on q-regular bipartite graphs: 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.<|reference_end|>
@article{sin2005on,
    title={On the dimensions of certain LDPC codes based on q-regular bipartite
  graphs},
    author={Peter Sin and Qing Xiang},
    journal={IEEE Trans. Information Theory, 52 (8), (2006), 3735-3737},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0506011},
    primaryClass={cs.IT cs.DM math.IT}
}