Bounds on the Pseudo-Weight of Minimal Pseudo-Codewords of Projective Geometry Codes
<|reference_start|>Bounds on the Pseudo-Weight of Minimal Pseudo-Codewords of Projective Geometry Codes: In this paper we focus our attention on a family of finite geometry codes, called type-I projective geometry low-density parity-check (PG-LDPC) codes, that are constructed based on the projective planes PG{2,q). In particular, we study their minimal codewords and pseudo-codewords, as it is known that these vectors characterize completely the code performance under maximum-likelihood decoding and linear programming decoding, respectively. The main results of this paper consist of upper and lower bounds on the pseudo-weight of the minimal pseudo-codewords of type-I PG-LDPC codes.<|reference_end|>
@article{smarandache2005bounds,
    title={Bounds on the Pseudo-Weight of Minimal Pseudo-Codewords of Projective
  Geometry Codes},
    author={Roxana Smarandache and Marcel Wauer},
    journal={arXiv preprint arXiv:cs/0510049},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0510049},
    primaryClass={cs.IT cs.DM math.IT}
}