Classification of Base Sequences BS n 1 , n Dragomir Ž

Base sequences BS n 1, n are quadruples of {±1}-sequences A;B;C;D , with A and B of length n 1 and C and D of length n, such that the sum of their nonperiodic autocor-relation functions is a δ-function. The base sequence conjecture, asserting that BS n 1, n exist for all n, is stronger than the famous Hadamard matrix conjecture. We introduce a new definition of equivalence for base sequences BS n 1, n and construct a canonical form. By using this canonical form, we have enumerated the equivalence classes of BS n 1, n for n ≤ 30. As the number of equivalence classes grows rapidly but not monotonically with n, the tables in the paper cover only the cases n ≤ 13.