On the base sequence conjecture
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 n=28,...,35. We also propose a conjecture describing these graphs in general.
Keywords
Cite
@article{arxiv.1003.1454,
title = {On the base sequence conjecture},
author = {Dragomir Z. Djokovic},
journal= {arXiv preprint arXiv:1003.1454},
year = {2010}
}
Comments
19 pages, 10 tables. To appear in Discrete Mathematics.