Classification of Base Sequences BS( n + 1, n )
Dragomir Ž. Ðoković
Source 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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