The spectrum for large sets of $(3,λ)$-GDDs of type $g^u$
In this paper, we completely solve the existence of large sets of $(3,λ)$-GDDs of type $g^u$ and the existence of a simple $(3,λ)$-GDD of type $g^u$.
math.CO↗
arXiv subjects
X. Niu
Publications and source records attributed to X. Niu.
Non-existence of perfect binary sequences
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For $n \equiv 1\pmod 4$, we prove some cases of Schmidt's Conjecture for perfect binary sequences. (Des. Codes Cryptogr. 78 (2016), 237-267.) For $n \equiv 2\pmod 4$, Jungnickel and Pott (Discrete Appl. Math. 95 (1999) 331-359.) left four perfect binary sequences as open problem and we solve three of its. For $n \equiv 3\pmod 4$, we present some nonexistence of binary sequences which all nontrivial autocorrelation values are equal 3. For $n \equiv 0\pmod 4$, we show that there do not exist the binary sequences which all nontrivial autocorrelation values are equal 4.
math.CO↗
Some results on generalized strong external difference families
A generalized strong external difference family (briefly $(v, m; k_1,\dots,k_m; λ_1,\dots,λ_m)$-GSEDF) was introduced by Paterson and Stinson in 2016. In this paper, we construct some new GSEDFs for $m=2$ and use them to obtain some results on graph decomposition. We also give some nonexistence results for GSEDFs. Especially, we prove that a $(v, 3;k_1,k_2,k_3; λ_1,λ_2,λ_3)$-GSEDF does not exist when $k_1+k_2+k_3< v$.
math.CO↗
Constructions and bounds for separating hash families
In this paper, we present a new construction for strong separating hash families by using hypergraphs and obtain some optimal separating hash families. We also improve some previously known bounds of separating hash families.
cs.IT↗
Some new bounds of placement delivery arrays
Coded caching scheme is a technique which reduce the load during peak traffic times in a wireless network system. Placement delivery array (PDA in short) was first introduced by Yan et al.. It can be used to design coded caching scheme. In this paper, we prove some lower bounds of PDA on the element and some lower bounds of PDA on the column. We also give some constructions for optimal PDA.
cs.IT↗