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.

In this work we apply the method for constructing binary LCD codes via an automorphism of prime order described in [3] and [4]. Thus we obtain all optimal LCD codes of lengths 26, 27 and 28 possessing an automorphism of order 13 with two cycles.

Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number we have classified all binary self-dual codes with length 76 having minimum distance d = 14 and automorphism of order 9. Up to equivalence, there are six self-dual [76, 38, 14] codes with an automorphism of type 9-(8, 0, 4). All codes obtained have new values of the parameter in their weight enumerator thus more than doubling the number of known values.

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