Classification of Base Sequences

Abstract

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