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Scholarly record

Symmetric Designs and Self-dual Codes

ERIC S. LANDER

Abstract

A construction is given for associating to any symmetric (v, k, X) design a self-dual code of length v+ 1 over GF (p), where p is any divisor of the square-free part of k — k. 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, X) design possesses an automorphism a of odd prime order q. If any prime dividing the square-free part of k — A has even (multiplicative) order mod q, then a must fix an odd number of points of the design.

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