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Zbl 0703.62076
Koukouvinos, C.; Kounias, S.; Sotirakoglou, K.
On base and Turyn sequences. (English)
[J] Math. Comput. 55, No.192, 825-837 (1990). ISSN 0025-5718; ISSN 1088-6842/e

Summary: Base sequences of lengths $n+1$, $n+1$, n, n are constructed for all decompositions of $4n+2$ into four squares for $n=19,...,24$. The construction is achieved through an algorithm which is also presented. It is proved through an exhaustive search that Turyn sequences do not exist for $n=18,...,27$; since Turyn sequences cannot exist for $n=28$ or 29 the first unsettled case is $n=30$.

MSC 2000:: *62K10 Statistical block designs
62K05 Optimal statistical designs
05B20 (0,1)-matrices (combinatorics)

Keywords: associate polynomial; autocorrelation; cross-correlation; construction; Base sequences; decompositions; four squares; algorithm; Turyn sequences

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