The extended binary quadratic residue code of length 42 holds a 3-design

01/08/2021

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by   Alexis Bonnecaze, et al.

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The codewords of weight 10 of the [42,21,10] extended binary quadratic residue code are shown to hold a design of parameters 3-(42,10,18). Its automorphism group is isomorphic to PSL(2,41). Its existence can be explained neither by a transitivity argument, nor by the Assmus-Mattson theorem.