Construction of self-dual codes with an automorphism of order p

We develop a construction method for finding self-dual codes with an automorphism of order p with c independent p-cycles. In more detail, we construct a self-dual code with an automorphism of type p- (c; f + 2) and length n+2 from a self-dual code with an automorphism of type p- (c; f) and length n, where an automorphism of type p- (c; f) is that of order p with c independent cycles and fixed points. Using this construction, we find three new inequivalent extremal self-dual [54; 27; 10] codes with an automorphism of type 7- (7; 5) and two new inequivalent extremal self-dual [58; 29; 10] codes with an automorphism of of type 7- (8; 2). We also obtain an extremal self-dual [40; 20; 8] code with an automorphism of type 3- (10; 10), which is constructed from an extremal self-dual [38; 19; 8] code of type 3- (10; 8), and at least 482 inequivalent extremal self-dual [58; 29; 10] codes with an automorphism of type 3- (18; 4), which is constructed from an extremal self-dual [54; 27; 10] code of type 3- (18; 0); we note that the extremality is preserved.