Further Results on the Optimal Sequence Family IP8 Over 8-Ary Q-PAM Constellation

A family IP8 of sequences over the 8-ary quadrature-pulse amplitude modulation (Q-PAM) constellation with asymptotically optimal correlation property was presented by Anand and Kumar in 2008. This is the only known family of sequences over the quadrature amplitude modulation (QAM) constellation whose correlation magnitude asymptotically achieves the Welch bound. In this paper, a larger family IP8new of sequences with the same correlation magnitude as that of IP8 but double family size is obtained. Moreover, the correlation distributions of IP8 and IP8new are also determined for two particular cases in terms of the property of a class of exponential sums over Galois rings. It is also shown that more classes of QAM and Q-PAM sequences with low correlation and larger family size can be obtained from our approach.