LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such is trying to avoid cycles short length in associated Tanner graph, i.e. obtaining a possibly large girth. In this paper, we provide framework obtain constructions codes. We relate criteria for existence certain some number-theoretic concepts, particul...

Safe, accessible, and good water quality are essential characteristics for reducing various waterborne diseases. Since domestic is the most consumed by Lebanese people, cleaning household tanks important to prevent their exposure pathogenic microorganisms. Generally, all stages of value chain sector still imperfect. Thus, should be regularly tested, especially in impoverished landmarks where wo...

S. A. Telyakovskiı̆ (1964, Izv. Akad. Nauk. SSR. Ser. Mat. 28, 1209–1236) proved an integrability condition for cosine series. No condition superior to that has been given so far. In this paper we identify the atomic structure of the Hardy type space that can be associated with this condition. As a consequence, we conclude that Telyakovskiı̆’s condition is equivalent to certain Sidon type inequal...