Abstract
We show that a p-ary polyphase sequence of period p2 from the Fermat quotients is ‘perfect.’ That is, its periodic autocorrelation is zero for all non-trivial shifts. We call this Fermat-Quotient sequences. Using this and the fact that the Frank-Zadoff sequences (which is known to be also perfect), we propose a collection of ‘optimum’ families of perfect polyphase sequences in the sense of Sarwate Bound. That is, the cross-correlation of two members in a family is upper bounded by p. We may say these families are ‘completely optimum’ since the cross-correlation of any two members in a family is exactly p for all phase-shifts.
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