Partial direct product difference sets and almost quaternary sequences

Abstract

In this paper, we study the $ m $-ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost $ m $-ary nearly perfect sequences. We show that these sequences are equivalent to $ \ell $-partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero-symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for $ \ell $-PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.