Title of article :
Super-Simple (v, 5, 2) Directed Designs and Their Smallest Defining Sets with Application in LDPC Codes
Author/Authors :
Mohammadnezhad ، Maryam Department of Mathematics - Faculty of Mathematical Sciences - Alzahra University , Golalizadeh ، Somayye Department of Mathematics - Faculty of Mathematical Sciences - Alzahra University , Boostan ، Mahsa Department of Mathematics - Faculty of Mathematical Sciences - Alzahra University , Soltankhah ، Nasrin Department of Mathematics - Faculty of Mathematical Sciences - Alzahra University
Abstract :
In this paper, we show that for all v ≡ 0, 1 (mod 5) and v ≥ 15, there exists a super-simple (v, 5, 2) directed design. Moreover, for these parameters, there exists a super-simple (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 :
Super , simple directed design , Trade , LDPC codes , Tanner graph
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
