Publication: On the base sequence conjecture

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Title	On the base sequence conjecture
Authors/Editors*	D.Z. Djokovic
Where published*	Discrete Mathematics
How published*	Journal
Year*	2010
Volume	310
Number
Pages	1956-1964
Publisher	Elsevier
Keywords	Base sequences, normal sequences, near-normal sequences,
Link	Djokovic, Dragomir
Abstract	Let BS(m,n) denote the set of base sequences (A;B;C;D), with A and B of length m and C and D of length n. The base sequence conjecture (BSC) asserts that BS(n+1,n) exist (i.e., are non-empty) for all n. This is known to be true for n <= 36 and when n is a Golay number. We show that it is also true for n=37 and n=38. It is worth pointing out that BSC is stronger than the famous Hadamard matrix conjecture. In order to demonstrate the abundance of base sequences, we have previously attached to BS(n+1,n) a graph Gamma_n and computed the Gamma_n for n <= 27. We now extend these computations and determine the Gamma_n for 28 <= n <= 35. We also propose a conjecture describing these graphs in general.