English

Super-simple $(v,5,2)$ directed designs and their smallest defining sets with its application in LDPC codes

Combinatorics 2022-07-13 v2

Abstract

In this paper, we show that for all v0,1v\equiv 0,1 (mod 5) and v15v\geq 15, there exists a super-simple (v,5,2)(v,5,2) directed design, also for these parameters there exists a super-simple (v,5,2)(v,5,2) directed design such that its smallest defining sets contain at least half of its blocks. Also, we show that these designs are useful in constructing parity-check matrices of LDPC codes.

Keywords

Cite

@article{arxiv.2007.13743,
  title  = {Super-simple $(v,5,2)$ directed designs and their smallest defining sets with its application in LDPC codes},
  author = {M. Mohammadnezhad and S. Golalizadeh and M. Boostan and N. Soltankhah},
  journal= {arXiv preprint arXiv:2007.13743},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1508.00098

R2 v1 2026-06-23T17:26:30.424Z