On the Automorphisms of Order 15 for a Binary Self-Dual [96, 48, 20] Code

The structure of binary self-dual codes invariant under the action of a cyclic group of order pq for odd primes p ̸= q is considered. As an application we prove the nonexistence of an extremal self-dual [96, 48, 20] code with an automorphism of order 15 which closes a gap in [2].

[1]  W. Cary Huffman.  Automorphisms of codes with applications to extremal doubly even codes of length 48 , 1982, IEEE Trans. Inf. Theory.

[2]  E. M. Rains,et al.  Self-Dual Codes , 2002, math/0208001.

[3]  Eric M. Rains,et al.  Shadow Bounds for Self-Dual Codes , 1998, IEEE Trans. Inf. Theory.

[4]  Patrick Solé,et al.  On the algebraic structure of quasi-cyclic codes I: Finite fields , 2001, IEEE Trans. Inf. Theory.

[5]  N. J. A. Sloane,et al.  An Upper Bound for Self-Dual Codes , 1973, Inf. Control..

[6]  H. Mattson,et al.  New 5-designs , 1969 .

[7]  J. Simonis.  MacWilliams identities and coordinate partitions , 1995 .

[8]  Javier de la Cruz,et al.  On Extremal Self-Dual Codes of Length 96 , 2011, IEEE Transactions on Information Theory.

[9]  W. Cary Huffman,et al.  Fundamentals of Error-Correcting Codes , 1975 .