Abstract
We study the complex p-ary perfect and nearly perfect sequences where p is an odd prime and show that the existence of such sequences is equivalent to the existence of certain kinds of difference sets. Using results from difference sets, there are no p-ary perfect sequences of length p3 for s ≥ 3, 2p3 for s≥1, and pq for prime q > p. Also, there are no ternary perfect sequences of length 3q1q2 for primes q1, q2 where 3< q1 < q2. Using the standard 'self-conjugate' conditions, more non-existence results on perfect and nearly perfect sequences are obtained. To summarise the works, tables of existence and non-existence of perfect and nearly perfect sequences of length n are listed for 2 ≤n≤50
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