On Wednesday, 24 August 2016 02:00:03 UTC+10, Dima Pasechnik wrote: > > Also, do I get it right that you have a new "generic" construction of > strongly regular graphs? > As you know, we are collecting them - would you be interested in adding it > into sage/graphs/generators/ ? >
Sorry for the delay in replying. I am pursuing the goal of classifying bent functions by their Cayley graphs. https://sites.google.com/site/paulleopardi/Leopardi-ACCMCC-2015-talk-revised.pdf?attredirects=0&d=1 To do this, at first I tried creating a large worksheet in SageMathCloud: https://cloud.sagemath.com/projects/80f4c9e7-8a37-4f59-82e7-aa179ec0b652/files/public/bent-functions-duals-Cayley-graphs-public.sagews This turned out to be too slow even for the ternary bent functions in 8 dimensions, so I am refactoring the code into smaller, faster pieces, and using Bliss: https://github.com/penguian/Boolean-Cayley-graphs The construction is the simple one described by (e.g.) Bernasconi and Codenotti 1999: http://ieeexplore.ieee.org/document/755000/ One key difference is that I only consider those f such that f(0)=0, to yield a simple undirected strongly regular graph, as per Lemma 12 of Bernasconi and Codenotti. Starting with a representative f of an Extended Affine (EA) equivalence class of bent functions in (Z_2)^{dim} -> Z_2, my code forms each g(x)=f(x+b)+<c,x>+f(b) for each b,c in (Z_2)^{dim}, and then lists the unique Cayley graphs found, yielding a list of Cayley graphs, and a matrix of indices. The code that performs this search is in https://github.com/penguian/Boolean-Cayley-graphs/blob/master/boolean_function_cayley_graph_classification.sage My starting point is known lists of representatives of EA equivalence classes of bent functions. So far, these are fully enumerated only up to ternary functions in dim=8. See (e.g.) Tokareva, Bent Functions, 2015, Chapter 7. http://store.elsevier.com/Bent-Functions/Natalia-Tokareva/isbn-9780128023181/ The web site http://langevin.univ-tln.fr/project/quartics/quartics.html lists quartic forms in dim=8, but this is apparently not sufficient to enumerate the EA equivalence classes ( Langevin and Leander 2011 http://link.springer.com/article/10.1007/s10623-010-9455-z ) Maybe my code could help to count these classes? -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
