A Survey of Base Sequences, Disjoint Complementary Sequences and $OD(4t;t,t,t,t)$

Abstract

We survey the existence of base sequences, that is, four sequences of lengths $m+p,m+p,m,m,p$ odd with zero auto-correlation function, which can be used with Yang numbers and four disjoint complementary sequences (and matrices) with zero non-periodic (periodic) auto-correlation function to form longer sequences. We survey their application to make orthogonal designs $OD(4t;t,t,t,t)$. We give the method of construction of $OD(4t;t,t,t,t)$ for $t=1,3,\dots ,41,45,\dots ,65,67$, $69,75,77,81,85,87,91,93,95,99,101,105$, $111,115,117,119,123,125,129,133,141,\dots ,147,153$, $155,159,161,165,169,171,175,177,183,185,189,195,201,203,205,209$.