摘要 : It is shown that the minimal distance d of a binary self-dual code of length n<or=74 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... 展开 It is shown that the minimal distance d of a binary self-dual code of length n<or=74 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 one to find the highest possible minimal distance of a self-dual code for all n<or=60; to show that self-dual codes with d>or=6 exist precisely for n<or=22, with d<or=8 exist precisely for n=24, 32 and n<or=26, and with d<or=10 exist precisely for n<or=46; and to show that there are exactly eight self-dual codes of length 32 with d=8. Several of the self-dual codes of length 34 have trivial group (this appears to be the smallest length where this can happen). 收起