Almost difference sets in nonabelian groups

Michel, Jerod; Wang, Qi

2019-06

10.1007/s10623-018-0519-9

DESIGNS CODES AND CRYPTOGRAPHY   影响因子和分区

0925-1022

1573-7586

We give two new constructions of almost difference sets. The first is a generic construction of (q2(q + 1), q(q2 -1), q(q2 -q -1), q2 -1) almost difference sets in certain groups of order q2(q + 1) (q is an odd prime power) having (Fq2, +) as a subgroup. This construction yields several infinite families of almost difference sets, many of which occur in nonabelian groups. The second construction yields (4p, 2p + 1, p, p -1) almost difference sets in dihedral groups of order 4p where p = 3 (mod 4) is a prime. Moreover, it turns out that some of the infinite families of almost difference sets obtained produce Cayley graphs which are Ramanujan graphs.

Difference set Almost difference set Nonabelian group

SCI ; EI

英语

第一 ; 通讯

National Science Foundation of China[11601220] ; National Science Foundation of China[61672015]

Computer Science ; Mathematics

Computer Science, Theory & Methods ; Mathematics, Applied

WOS:000468552800001

SPRINGER

20183005601914

Computer applications ; Mathematical techniques

Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

COMPUTER SCIENCE

Web of Science

Southern Univ Sci & Technol, Dept Comp Sci & Engn, Shenzhen 518055, Peoples R China

Michel, Jerod,Wang, Qi. Almost difference sets in nonabelian groups[J]. DESIGNS CODES AND CRYPTOGRAPHY,2019,87(6):1243-1251.

Michel, Jerod,&Wang, Qi.(2019).Almost difference sets in nonabelian groups.DESIGNS CODES AND CRYPTOGRAPHY,87(6),1243-1251.

Michel, Jerod,et al."Almost difference sets in nonabelian groups".DESIGNS CODES AND CRYPTOGRAPHY 87.6(2019):1243-1251.