Sidelnikov (1969) have constructed an M-ary Sequence of period q-1 with good
autocorrelation, where M|q-1. Song (2007) has for the first time constructed a
sequence family including a Sidelnikov sequence and its constant multiples
with
good cross-correlation property. No (2008) and Yang (2009) have independently
constructed larger size families using Shift-and-Add, which is the method of
constructing the binary Gold sequences. Gong (2010) has constructed still
larger
size family using the array structure of a Sidelnikov sequence of period
$q^2-1$.
Recently, we are able to generalize this for a Sidelnikov sequence of period
$q^d-1$ and observed that its array structure works also. We will review these
constructions by many others, and describe the generalization in detail.