Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series B, Pt. 2, pp. 221--230

NEW WEIGHING MATRICES

By

CHRISTOS KOUKOUVINOS, National Technical University of Athens

and

JENNIFER SEBERRY, University of Wollongong

SUMMARY.  New weighing matrices and skew weighing matrices are given for many orders $4t{\leq}100$. These are constructed by finding new sequences with zero autocorrelation. These results enable us to determine for the first time that for $4t{\leq}84$ a W(4t, k)  exists for all k = 1, ..., 4t-1 and also that there exists a skew-weighing matrix (also written as an OD(4t; 1, k)) for $4t{\leq}80$, t odd, k=a2 +b2+c2, a, b, c integers except k=4t-2 must be the sum of two squares.

AMS (1980) subject classification.  Primary 62K05, 62K10, secondary 05B20.

Key words and phrases. Autocorrelation, construction, associated polynomial, sequence.

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