On a class of almost perfect sequences
An \(n\)-periodic sequence \((s_i)\) with entries \(\pm1\) is almost perfect if all but one of the sums \(\sum^{n-1}_{i=0} s_is_{i+1}\) (\(t\not\equiv 0\pmod n\)) are zero. Any almost perfect sequence is equivalent to a cyclic difference set in \(\mathbb{Z}_n\) of size \(k={n\over 2}-\theta\) and \(\lambda_1=\theta(\theta-1)\), \(\lambda_2={n\over 4}-\theta\). The paper proves some necessary conditions for the existence of such difference sets and sequences. In particular, it is shown that if \(\theta=2\), there are only 6 possible values for \(n\) in the range \(n\leq 20,000\).
scientific article; zbMATH DE number 1038260