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

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Nondegenerate quadrics of PG (2l, 2^{s}) have been used to construct ternary sequences of length (2^{2\sl+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) , with N arbitrary and q = p^{s} , for any prime p . This is possible because it is shown that if Q \subseteq {\rm PG} (N, q) is a quadric, possibly degenerate, that has the same size as a hyperplane, then, provided Q itself is not a hyperplane, the hyperplanes of PG (N,q) intersect Q in three sizes. These sizes depend on whether N is even or odd and the degeneracy of Q . Finally, a connection to maximum period linear recursive sequences is made.

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IEEE Transactions on Information Theory  (Volume:32 ,  Issue: 3 )