Self-dual codes with an automorphism of order 17
Müberra Gürel, Nikolay Yankov · University of Zagreb University Computing Centre (SRCE) · 2015
In this paper, we study optimal binary self-dual codes with minimum distance 12 having an automorphism of order 17.We prove that all such codes have parameters [68 + f, 34 + f /2, 12], f = 0, 2, 4 and an automorphism of type 17 -(4, f ), f = 0, 2, 4 and provide a full classification of these codes.This classification gives new values β = 17, 153, 170, 187, 221, 255 for γ = 0 in the weight enumerator W68,2 of [68, 34, 12] codes; new values β = 102, 136, 170, 204, 238, 272, 306, 340, 374, 408, 442, 476, 510, 544, 578, and 612 for γ = 0 in W70,1 of [70, 35,12] codes; and numerous singly-even and doubly-even [72, 36,12] codes with new parameters in their weight enumerators.