# On the base sequence conjecture - Mathematics > Combinatorics

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Abstract: Let BSm,n denote the set of base sequences A;B;C;D, with A and B oflength m and C and D of length n. The base sequence conjecture BSC assertsthat BSn+1,n exist i.e., are non-empty for all n. This is known to be truefor n <= 36 and when n is a Golay number. We show that it is also true for n=37and n=38. It is worth pointing out that BSC is stronger than the famousHadamard matrix conjecture. In order to demonstrate the abundance of basesequences, we have previously attached to BSn+1,n a graph Gamma n andcomputed the Gamma n for n <= 27. We now extend these computations anddetermine the Gamma n for n=28,

.,35. We also propose a conjecture describingthese graphs in general.

Author: ** Dragomir Z. Djokovic**

Source: https://arxiv.org/