Author/Authors :
Xia ، Tianbing School of Computing and Information Technology, Faculty of Engineering and Information Sciences - University of Wollongong , Xia ، Mingyuan School of Computing and Information Technology, Faculty of Engineering and Information Sciences - University of Wollongong , Seberry ، Jennifer School of Mathematics and Statistics - Central China Normal University
Abstract :
For every prime power q≡7mod16 , there are (q; a, b, c, d)-partitions of GF(q), with odd integers a, b, c, and d, where a≡±1mod8 such that q=a2+2(b2+c2+d2) and d2=b2+2ac+2bd . Many results for the existence of 4−{q2;q(q−1)/2;q(q−2)} SDS which are simple homogeneous polynomials of parameters a, b, c and d of degree at most 2 have been found. Hence, for each value of q, the construction of SDS becomes equivalent to building a (q;a,b,c,d) -partition. Once this is done, the verification of the construction only involves verifying simple conditions on a, b, c and d which can be done manually.
