Symmetric Designs and Self-Dual Codes
Eric S. Lander · Journal of the London Mathematical Society · 1981
A construction is given for associating to any symmetric (v, k,λ) design a self-dual code of length v+ 1 over GF (p), where p is any divisor of the square-free part of k−λ. These codes are then used to obtain a substantial strengthening of a result of Hughes on automorphisms of designs. Specifically, suppose a symmetric (v, k,λ) design possesses an automorphism σ of odd prime order q. If any prime dividing the square-free part of k−λ has even (multiplicative) order mod q, then a must fix an odd number of points of the design.