Even-shift orthogonal sequences

A class of binary sequences whose elements are either1or-1and whose autocorrelation function is0for all even shifts except the zero shift is discussed. These sequences will be calledEsequences. It is proved that everyEsequence is paired with anotherEsequence, its mate, so that the cross-correlation function between them is0for all even shifts including the zero shift. Using these sequences, new complete orthogonal function sets are derived. Several other important properties of these sequences are also obtained and the relations among these sequences, Golay's complementary sequences and Welti's quaternary codes are discussed.