Abstract
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.
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