On non-existence of perfect and nearly perfect sequences
type: Item
instance of: scholarly article
title: On non-existence of perfect and nearly perfect sequences
zbMATH Open document ID: 1219.11042
DOI: 10.1504/IJICOT.2009.024045
author: Siu Lun Ma
author: Wei Shean Ng
published in: International Journal of Information and Coding Theory
publication date: 2011-02-04T00:00:00Z
review text: Summary: 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 \(s\geq 3 \), \(2p^s \) for \(s\geq 1 \), and \(pq\) for prime \(q>p\). Also, there are no ternary perfect sequences of length \(3q_1q_2 \) for primes \(q_1,q_2 \) where \(3<q_1<q_2 \). 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 \(2\leq n\leq 50\).
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 5845397
zbMATH Keywords: perfect sequence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5845397