2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with by Bouyukliev I., Fack V., Winne J.

By Bouyukliev I., Fack V., Winne J.

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Additional info for 2-(31,15,7), 2-(35,17,8) and 2-(36,15,6) designs with automorphisms of odd prime order, and their related Hadamard matrices and codes

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There are at least di-1 non-crossing moves between mi and m, because one single move can shorten a decreasing string by at most one element at each end. After the move m the nearer end of the newly created maximal increasing substring straddling the barrier has distance one from the barrier, because m must involve reversing a substring which is adjacent to but not crossing the barrier. 11. Slope problems 41 at each end. Altogether, therefore, there are at least (di - 1) + 1 + (di+1 - 1) non-crossing moves between m2 and mi+i We will need one more fact: (3) there are at least dt + d1 - 1 non-crossing moves after mt and before ml.

In general, the signed cocircuit of a hyperplane ijk is computed as Y2jk = (Y+,Y-) where Y+ = { e E E : X(i, j, k, e) =+I and Y- = { e E E : X(i, j, k, e) =-J. 5. Recall that if i, j, k, e are out of order, we adjust the sign from the above chirotope listing according to the sign of the appropriate permutation. 5. Realizability 23 Note that it is easy to determine the facet triangles from this list: they are exactly the complements of positive (or negative) cocircuits. A realization of RS(8) is a labeled subset {xi, ...

Can you find a similar condition for t and ' to determine the same oriented matroid?

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