Design theory
On (pa, p, pa, pa−1)-relative difference sets
Designs, Codes and Cryptography
A survey on relative difference sets
GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster
On Circulant Complex Hadamard Matrices
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Almost p-ary perfect sequences
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Sequences and functions derived from projective planes and their difference sets
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Nonexistence of certain almost p-ary perfect sequences
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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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 3q1 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