Recently, we have found in 2016 (IT Trans, Park, Song, Kim, Golomb)
that, for any odd prime p,
a p-ary polyphase sequence of period p^2 
using the Fermat-quotients is perfect.

It turned out that this new perfect sequence is a special case 
of the generalized bent function sequences 
by Kumar, Scholtz, and Welch in 1985.

Another special case is p-ary Frank-Zadoff sequence of period p^2, 
which is also a perfect polyphase sequence,
and this is defined for any positive integer N including prime p.

On the other hand, we found a construction for an optimal family
of perfect sequences including those using Fermat-quotient. 
It turned out that not all perfect sequences can make such an optimal family.
We have identified a necessary and sufficient condition for
a perfect sequence to be used to construct an optimal family, and
found an algebraic and systematic construction for such perfect sequences.
Of course, all these idea is generalized to all the positive integers, 
prime or not, and the results is summarized in a recently accepted paper 
in a special issue of IT Transactions in memory of Prof. Golomb.