The geometry of quadrics and correlations of sequences (Corresp.)

Nondegenerate quadrics of PG have been used to construct ternary sequences of length with perfect autocorrelation function. The same construction can be used for degenerate quadrics for this case as well as quadrics of PG , with arbitrary and , for any prime . This is possible because it is shown that if is a quadric, possibly degenerate, that has the same size as a hyperplane, then, provided itself is not a hyperplane, the hyperplanes of PG intersect in three sizes. These sizes depend on whether is even or odd and the degeneracy of . Finally, a connection to maximum period linear recursive sequences is made.