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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 ...
Cyclic codes over GR(p2,m) of length pk
We study cyclic codes of length pk over GR(p2,m), or equivalently, ideals of the ring GR(p2,m)/ upk − 1 . We derive a method of representing the ideals, and classify all ideals in the ring GR(p2,m)/upk −1 . We also analyse ...