Tuesday, September 2, 2008


Also known as incidence structures, nonlinear binary codes, block designs and (0,1)-matrices... The object is a collection of points P, and a collection of blocks, which are subsets of P. The action of S_P induces an action on subsets of P, and the subgroup of S_P which takes blocks to blocks is the automorphism group of the incidence structure.

This is the latest application of the generalized partition backtrack methods for computing automorphism groups and canonical labels. It is implemented with surprising similarity to the linear case (for example, the exact same refinement procedure is used). In fact, one of the optimizations Leon uses is to take some subset of the words of a linear binary code, and use them for refinement. With this new code in place, it will be trivial to implement such an optimization. However, choosing which subset of blocks, and then finding them all, is not a simple problem -- his approach is to simply take the set of words of minimum weight. This does reduce the time taken to refine each partition substantially, but it may have unexpected adverse effects of enlarging the search tree, depending on the specific code.

Currently the code is valgrinding to find the usual segfaults and other human errata. Then there should be a patch appearing soon on trac. Thanks again to Google for funding all this!

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