Classification of Base Sequences BS(n+1,n)‎

Abstract EN

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.Erratum of “Classification of Base Sequences BS(n+1,n)”dx.doi.org/10.1155/2010/842636