Equivalence classes and representatives of Golay sequences Original Research Article

We introduce the notion of canonical form for Golay sequences such that every equivalence class contains exactly one member having the canonical form. Golay and Turyn have shown how to multiply Golay sequences of length m with Golay sequences of length n in order to construct Golay sequences of length mn. We say that Golay sequences of length n are constructible if they can be manufactured from Golay sequences of length < n by using the multiplication operation and the elementary transformations. We list representatives of the equivalence classes of Golay sequences for all lengths ⩽40 and determine which classes are constructible.