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Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,lambda_a,1)$-OOSPC with $lambda_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,lambda_a,1)$-OOSPC is determined for any positive integers $m,nequiv2 ({rm mod } 4)$ and $lambda_ain{2,3}$.
Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code-division multiple-access (CDMA) network for 2-dimensional image transmission. There is a one-to-one correspondence between an $(m, n, w, lambda
In this paper we investigate combinatorial constructions for $w$-cyclic holely group divisible packings with block size three (briefly by $3$-HGDPs). For any positive integers $u,v,w$ with $uequiv0,1~(bmod~3)$, the exact number of base blocks of a ma
How can $d+k$ vectors in $mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define $theta(d,k):=min_Xmax_{x eq yin X}|langle x,yrangle|$ where the minimum is taken over all collections of $d+k$ unit vectors
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with sma
We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an algorithmic method