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 -partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zerosymbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for -PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.