The geometry of quadrics and correlations of sequences (Corresp.)
Richard A. Games · IEEE Transactions on Information Theory · 1986
Nondegenerate quadrics of PG(2l, 2^{s})have been used to construct ternary sequences of length(2^{2sl+1} - 1)/(2^{s} - 1)with perfect autocorrelation function. The same construction can be used for degenerate quadrics for this case as well as quadrics of PG(N,q), withNarbitrary andq = p^{s}, for any primep. This is possible because it is shown that ifQ \subseteq {\rm PG} (N, q)is a quadric, possibly degenerate, that has the same size as a hyperplane, then, providedQitself is not a hyperplane, the hyperplanes of PG(N,q)intersectQin three sizes. These sizes depend on whetherNis even or odd and the degeneracy ofQ. Finally, a connection to maximum period linear recursive sequences is made.