Name
Abstract | ||
|---|---|---|
A generalized strong external difference family (briefly \((v, m; k_1,\dots ,k_m; \lambda _1,\dots ,\lambda _m)\)-GSEDF) was introduced by Paterson and Stinson in 2016. In this paper, we give some nonexistence results for GSEDFs. In particular, we prove that a \((v, 3;k_1,k_2,k_3; \lambda _1,\lambda _2,\lambda _3)\)-GSEDF does not exist when \(k_1+k_2+k_3< v\). We also give a first recursive construction for GSEDFs and prove that if there is a \((v,2;2\lambda ,\frac{v-1}{2};\lambda ,\lambda )\)-GSEDF, then there is a \((vt,2;4\lambda ,\frac{vt-1}{2};2\lambda ,2\lambda )\)-GSEDF with \(v>1\), \(t>1\) and \(v\equiv t\equiv 1\pmod 2\). Then we use it to obtain some new GSEDFs for \(m=2\). In particular, for any prime power q with \(q\equiv 1\pmod 4\), we show that there exists a \((qt, 2;(q-1)2^{n-1},\frac{qt-1}{2};(q-1)2^{n-2},(q-1)2^{n-2})\)-GSEDF, where \(t=p_1p_2\dots p_n\), \(p_i>1\), \(1\le i\le n\), \(p_1, p_2,\dots ,p_n\) are odd integers. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10623-018-0481-6 | Des. Codes Cryptography |
Keywords | Field | DocType |
Generalized strong external difference family, Difference set, Character theory, Nonexistence, 05B05, 05B10 | Integer,Discrete mathematics,Combinatorics,Character theory,Difference set,Prime power,Mathematics,Lambda | Journal |
Volume | Issue | ISSN |
86 | 12 | 0925-1022 |
Citations | PageRank | References |
1 | 0.36 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiaojuan Lu | 1 | 1 | 0.36 |
| Xiaolei Niu | 2 | 2 | 2.12 |
| H. Cao | 3 | 47 | 8.15 |