In this paper, two new modulation schemes using multilevel pulse-position modulation (PPM) for application in unipolar optical wireless systems are presented. Balanced incomplete block designs (BIBD) are used for constructing the symbol alphabets. Each symbol is obtained by combining multiple codewords of a BIBD code. In one scheme the symbols have equal energies, and therefore, no threshold is...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v, 3, λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v, 3, λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if...

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in constructing codes and designs such as superimposed codes and perfect hash families. The existence of super-simple (v, 4, λ)BIBDs have been determined for λ = 2, 3, 4, 5, 6. In this paper, we investigate the existence...

BIBD (balanced incomplete block design) is instrumental in design of experiments. This is usually constructed using algebraic tools such as finite projective (or affine) algebra or difference sets. Recently, heuristic algorithms have been tried, including artificial neural networks, simulated annealing, and local search method. In this paper, we present a novel approach to construct BIBDs that ...

In this paper, we investigate the PBD-closure of sets K with {7, 13} ⊆ K ⊆ {7, 13, 19, 25, 31, 37, 43}. In particular, we show that v ≡ 1 mod 6, v ≥ 98689 implies v ∈ B({7, 13}). As a preliminary result, many new 13-GDDs of type 13q and resolvable BIBD with block size 6 or 12 are also constructed. Furthermore, we show some elements to be not essential in a Wilson bases for the PBD-closed set {v...

Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification) information from one of the two sets to ...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...