Binary self-dual codes with automorphisms of order 23

The only example of a binary doubly-even self-dual [120,60,20] code was found in 2005 by Gaborit et al. (IEEE Trans Inform theory 51, 402–407 2005). In this work we present 25 new binary doubly-even self-dual [120,60,20] codes having an automorphism of order 23. Moreover we list 7 self-dual [116,58,18] codes, 30 singly-even self-dual [96,48,16] codes and 20 extremal self-dual [92,46,16] codes. All codes are new and present different weight enumerators.

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

[2]  Vassil Y. Yorgov.  A method for constructing inequivalent self-dual codes with applications to length 56 , 1987, IEEE Trans. Inf. Theory.

[3]  N. J. A. Sloane,et al.  A new upper bound on the minimal distance of self-dual codes , 1990, IEEE Trans. Inf. Theory.

[4]  A. Nijenhuis.  Combinatorial algorithms , 1975 .

[5]  Marcus Greferath,et al.  On two doubly even self-dual binary codes of length 160 and minimum weight 24 , 2005, IEEE Transactions on Information Theory.

[6]  Sophia Antipolis,et al.  Type I1 Codes over F4 , 2002 .

[7]  Masaaki Harada,et al.  Extremal binary self-dual codes , 1997, IEEE Trans. Inf. Theory.

[8]  Anton Betten,et al.  Codierungstheorie : Konstruktion und Anwendung linearer Codes , 1998 .

[9]  Radinka Yorgova.  Binary self-dual extremal codes of length 92 , 2006, 2006 IEEE International Symposium on Information Theory.

[10]  Alfred Wassermann,et al.  On the weight enumerators of duadic and quadratic residue codes , 2004, IEEE Transactions on Information Theory.

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

[12]  A. Kerber,et al.  Error-correcting linear codes : classification by isometry and applications , 2006 .

[13]  Radinka Dontcheva,et al.  On the doubly-even self-dual codes of length 96 , 2002, IEEE Trans. Inf. Theory.

[14]  Masaaki Harada,et al.  An extremal singly even self-dual code of length 88 , 2007, Adv. Math. Commun..

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

[16]  P. Gaborit,et al.  Experimental constructions of self-dual codes , 2003 .