**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=a^{2 }+b^{2}+c^{2}, 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.