Classification of base sequences BS(n+1,n)
Combinatorics
2010-10-12 v3
Abstract
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 <= 30. Due to excessive size of the equivalence classes, the tables in the paper cover only the cases n <= 13.
Cite
@article{arxiv.1002.1414,
title = {Classification of base sequences BS(n+1,n)},
author = {Dragomir Z. Djokovic},
journal= {arXiv preprint arXiv:1002.1414},
year = {2010}
}
Comments
27 pages, 7 tables. Final version. To appear in the International Journal of Combinatorics.