maxSO7dim:=function(n) if n mod 4 eq 0 then d:=n div 2; elif n mod 2 eq 0 then d:=(n-2) div 2; else d:=(n-1) div 2; end if; return d; end function; massformula:=function(n) d:=maxSO7dim(n); e:=n-2*d; return &*[7^(d+e-i-1)+1:i in [0..d-1]]; end function; automorphismGroupPlusMinus1:=function(C); G:=AutomorphismGroup(C); n:=Length(C); return Stabilizer(G,&join{{1+6*i,6+6*i}:i in {0..n-1}}); end function; check:=function(n,CS) d:=maxSO7dim(n); return &and[IsSelfOrthogonal(x): x in CS] and &and[Dimension(x) eq d: x in CS] and &+[2^n*Factorial(n)/#automorphismGroupPlusMinus1(C):C in CS] eq massformula(n) and &and{&and{not IsEquivalent(CS[i],CS[j]):j in {i+1..#CS}} :i in {1..#CS}}; end function; load "4.magma"; check(4,codes); load "8.magma"; check(8,codes); load "12.magma"; check(12,codes);