On the automorphism group of extremal codes of length 24m
Vortrag von Prof. Dr. Javier de la Cruz
Sprecher eingeladen von: Prof. Dr. Joachim Rosenthal
Datum: 08.12.14 Zeit: 13.00 - 14.00 Raum: UNINE, B217
Click here to download the abstract as pdfIn this work we study the automorphism group of extremal codes of lengths 96 and 120. First we prove that an automorphism of an extremal [96, 48, 20] code C of order 3 has exactly 6 or no fixed points and an automorphism of order 5 has exactly 6 fixed points. Moreover, if all automorphisms of order 3 are fixed point free then either Aut(C) is a solvable group and its order is 15, 30, 240, 480 or divides 2^5*3, 2^5*5, or Aut(C) is the alternating group A_5 . Furthermore, |Aut(C)| = 20 or |Aut(C)| = 40 cannot occur.
Moreover we prove that the only odd primes that may divide the order of the automorphism group of a putative binary self-dual doubly-even [120, 60, 24] code C are 2, 3, 5, 7, 19 and 23. Moreover, the cyclic structure of an automorphism of these orders is given by 3-(40; 0), 5-(24; 0), 7-(17;1), 19-(6;6) and 23-(5;5). The order of the automorphism group is |Aut(C)| = 2^a*3^b*5^c*7^d*19^e*23^f , where a ∈ N_0 and b, c, d, e, f ∈ {0,1}. Furthermore, we prove that if σ is an automorphism of C of odd composite order r then r = 15, 57 or r = 115 and the cyclic structure of an automorphism of these orders are given by 3*5-(0,0,8;0), 3*19-(2,0,2;0) or 5*23-(1,0,1;0).
The results are based on joint work with S. Bouyuklieva, M. Kiermaier, A. Wassermann and W. Willems.