On non-existence of perfect and nearly perfect sequences
by Siu Lun Ma, Wei Shean Ng
International Journal of Information and Coding Theory (IJICOT), Vol. 1, No. 1, 2009

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 p^s for s ≥ 3, 2p^s, 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.

Online publication date: Tue, 24-Mar-2009

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