Monitoring the long-distance pipelines, rivers, roads and boundary lines with wireless sensor networks belongs to one-dimensional region monitoring. This paper primarily studies the coverage problems of the sensor networks in one-dimensional regions. Firstly, the onedimensional random coverage model is processed for the sensor nodes in one-dimensional monitoring region, and a formula is given t...

It is proved that codes of length n, covering radius Z?, and minimum Hamming distance 2R-1 are normal if R does not divide n. Constructions for abnormal codes with covering radius R and minimum Hamming distance at least R-l are given.

Let [ ] denote a linear code over with length , codimension , and covering radius . We use a modification of constructions of [2 +1 2 3] 2 and [3 +1 3 5] 3 codes ( 5) to produce infinite families of good codes with covering radius 2 and 3 and codimension .

The multicovering radii of a code are recent generalizations of the covering radius of a code. For positive m, the m-covering radius of C is the least radius t such that every m-tuple of vectors is contained in at least one ball of radius t centered at some codeword. In this paper upper bounds are found for the multicovering radii of first order Reed-Muller codes. These bounds generalize the we...

The length function $ \ell_q(r,R) is the smallest of a q $-ary linear code with codimension (redundancy) r and covering radius R $. In this work, new upper bounds on \ell_q(tR+1,R) are obtained in following forms:$ \begin{equation*} \begin{split} &(a)\; \ell_q(r,R)\le cq^{(r-R)/R}\cdot\sqrt[R]{\ln q},\; R\ge3,\; = tR+1,\; t\ge1,\\ &\phantom{(a)\; } q\;{\rm{ \;an\; arbitrary \;prime\; po...

In a recent paper by this author, constructions of linear binary covering codes are considered. In this work, constructions and techniques of the earlier paper are developed and modified for q-ary linear nonbinary covering codes, q 2 3, and new constructions are proposed. The described constructions design an infinite family of codes with covering radius R based on a starting code of the same c...

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...