A new method to construct golay complementary set and near-complementary set by paraunitary matrices

We present our previous work in [17] in a more generic way to construct q-ary Golay complementary sets and near-complementary sets of size N and sequence length M · Nm by using different seed sequences, where m is an arbitrary non-negative integer, M is the length of seed sequences and N is a power of 2. The boolean functions of these sequences will also be derived with our method. To illustrate it, we will derive a new quaternary Golay set that has never been recorded before, and we will rephrase the boolean functions of near complementary sequences presented in Theorem 12 [9] by our method.