A New Upper Bound on the Minimal Distance of Self-Dual Codes.

It is shown that the minimal distance d of a binary self-dual code of length n >= 48 is at most 2 [(n+6)/10]. This bound is a consequence of some new conditions on the weight enumerator of a self-dual code obtained by considering a particular translate of the code called its "shadow". These conditions also enable us to find the highest possible minimal distance of a self- dual code for all n = 6 exist precisely for n >= 22, with d >= 8 exist precisely for n = 24, 32 and n >=36, and with d>= 10 exist precisely for n >= 46; and to show that there are exactly eight self- dual codes of length 32 with d = 8.