Abstract

We examine a design D and a binary code C constructed from a primitive permutation representation of degree 275 of the sporadic simple group M c L . We prove that Aut ( C ) = Aut ( D ) = M c L : 2 and determine the weight distribution of the code and that of its dual. In Section 5, we show that for a word w i of weight i , where i ∈ { 100 , 112 , 164 , 176 } the stabilizer ( M c L ) w i is a maximal subgroup of M c L . The words of weight 128 splits into three orbits C ( 128 ) 1 , C ( 128 ) 2 and C ( 128 ) 3 , and similarly the words of weights 132 produces the orbits C ( 132 ) 1 and C ( 132 ) 2 . For w i ∈ { C ( 128 ) 1 , C ( 128 ) 2 , C ( 132 ) 1 } , we prove that ( M c L ) w i is a maximal subgroup of M c L . Further in Section 6, we deal with the stabilizers ( M c L : 2 ) w i by extending the results of Section 5 to M c L : 2 .

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