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Constructions of relative difference sets with classical parameters and circulant weighing matrices
In this paper, a new family of relative difference sets with parameters (m,n,k,λ)=((q^7-1)/(q-1), 4(q-1), q^6, q^5/4) is constructed where q is a 2-power. The construction is based on the technique used in . By ...
New hadamard matrices of order 4p^2 obtained from Jacobi sums of order 16
Let p=7 mod 6 be a prime. Then there are integers a,b,c,d with a=15 mod 6, b= 0 mod 4, p^2=a^2+2(b^2+c^2+d^2), and 2ab=c^2-2cd-d^2. We show that there is a regular Hadamard matrix of order 4p2 provided that p=a±2b or ...
Constructions of semi-regular relative difference sets
J. A. Davis, J. Jedwab, and M. Mowbray (1998, Des. Codes Cryptogr. 13, 131-146) gave two new constructions for semi-regular relative difference sets (RDSs). They asked if the two constructions could be unified. In this ...