Classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order

The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48,24,10] code with an automorphism of type p-(c,f) with p being an odd prime, then p=3, c=16, f=0. By considering only an automorphism of type 3-(16,0), we prove that there are exactly 264 inequivalent self-dual [48,24,10] codes with an automorphism of odd prime order, equivalently, there are exactly 264 inequivalent cubic self-dual [48,24,10] codes.