Correlation of binary sequence families derived from the multiplicative characters of finite fields
Zilong Wang, Guang Gong · Advances in Mathematics of Communications · 2013
In this paper, new constructions of the binary sequence families ofperiod $q-1$ with large family size and low correlation, derivedfrom multiplicative characters of finite fields for odd primepowers, are proposed. For $m ≥ 2$, the maximum correlationmagnitudes of new sequence families $\mathcal{S}_m$ are bounded by$(2m-2)\sqrt{q}+2m+2$, and the family sizes of $\mathcal{S}_m$ aregiven by $q-1$ for $m=2$, $2(q-1)-1$ for $m=3$,$(q^2-1)q^{\frac{m-4}{2}}$ for $m$ even, $m>2$, and$2(q-1)q^{\frac{m-3}{2}}$ for $m$ odd, $m>3$. It is shown that theknown binary Sidel'nikov-based sequence families are equivalent tothe new constructions for the case $m=2$.