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

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Title Classification of Base Sequences BS(n+1,n)
Authors/Editors* D.Z. Djokovic
Where published* International Journal of Combinatorics
How published* Journal
Year* 2010
Volume 2010
Pages 21 pages
Publisher Hindawi Publishing Corporation
Keywords Base sequences, nonperiodic autocorrelation function, canonical form
Base sequences BS(n+1,n) are quadruples of {+1,-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 autocorrelation functions is a delta-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 at most 30. As the number of equivalence classes grows rapidly (but not monotonically) with n, the tables in the paper cover only the cases of n up to and including 13.
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