On the size of the symmetry group of a perfect code

It is shown that for every nonlinear perfect code C of length n and rank r with n-log(n+1)[email protected][email protected]?n-1, |Sym(C)|@?|GL(n-r,2)|@?|GL(log(n+1)-(n-r),2)|@?(n+12^n^-^r)^n^-^r, where Sym(C) denotes the group of symmetries of C. This bound considerably improves a bound of Malyugin.

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