Relative ( pn , p , pn , n )-difference sets with GCD ( p , n )=1
Tao Feng
Peking University School of Mathematical Sciences Beijing 100871 People's Republic of China
DOI: 10.1007/s10801-008-0124-5
Abstract
Let p be an odd prime. We first get some non-existence and structural results on ( pn, p, pn, n) relative difference sets with gcd( p, n)=1 through a group ring approach. We then give a construction of ( p( p+1), p, p( p+1), p+1) relative difference sets with p a Mersenne prime.
Pages: 91–106
Keywords: keywords relative difference set; group ring; semi-regular relative difference set
Full Text: PDF
References
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2. Berndt, B.C., Evans, R.J., Williams, K.S.: Gauss and Jacobi Sums. Wiley, New York (1998)
3. Davis, J.A., Jedwab, J., Mowbray, M.: New Families of semi-regular relative difference sets. Des. Codes Cryptogr. 13, 131-146 (1998)
4. Feng, T., Xiang, Q.: Semi-regular relative difference sets with large forbidden subgroups. Submitted
5. Hiramine, Y.: Planar functions and related group algebras. J. Algebra 15, 135-145 (1992)
6. Hou, X.D.: p-ary and q-ary versions of certain results about bent functions and resilient functions.