The q -ary Golay arrays of size 2× 2×⋯× 2 are standard

To find the non-standard binary Golay sequences of length 2^m or theoretically prove their nonexistence are still open. It has been shown that all the standard q -ary ( q even) Golay sequence pairs of length 2^m can be obtained by q -ary Golay array pairs of dimension m and size 2× 2 ×⋯× 2 of a particular algebraic normal form. We extend the appellation “standard" from sequences to arrays and call the Golay array pairs of this algebraic normal form standard. It’s natural to ask whether all the q -ary Golay array pairs of size 2× 2 ×⋯× 2 are standard. We give a positive answer to this question.