Even-shift orthogonal sequences

A class of binary sequences whose elements are either
1
or
-1
and whose autocorrelation function is
0
for all even shifts except the zero shift is discussed. These sequences will be called
E
sequences. It is proved that every
E
sequence is paired with another
E
sequence, its mate, so that the cross-correlation function between them is
0
for 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.