The $q$-ary Golay complementary arrays of size $2^{(m)}$ are standard

Abstract

To find the non-standard binary Golay complementary sequences (GCSs) of length $2^m$ or theoretically prove the nonexistence of them are still open. Since it has been shown that all the standard $q$-ary (where $q$ is even) GCSs of length $2^m$ can be obtained by standard $q$-ary Golay complementary array pair (GAP) of dimension $m$ and size $2\times 2\times \cdots \times 2$ (abbreviated to size $2^{(m)}$), it's natural to ask whether all the $q$-ary GAP of size $2^{(m)}$ are standard. We give a positive answer to this question.