Анотация: The aim of this paper is to try to find new optimal self-dual codes of lengths 64 and 66 using previously known codes. We begin with an outline of the previous results regarding codes of these lengths. We then extend some known binary self-dual codes of length 62 to singly-even binary self-dual [64,32,12] codes using a known method of Harada and Kimura. As a result we find 8 new singly-even binary self-dual [64,32,12] codes and discuss their connection to the codes of length 62. We conclude with another result by extending the doubly-even [64,32,12] self-dual codes with an automorphism of type 31-(2, 2) to 35 new [66,33,12] self-dual codes. Two of these new codes that we obtain have an automorphism of type 5-(12, 6) and codes with this type of automorphism previously were not known to exist

Забележки: Наградени доклади ` Best Paper ` от 2016 г.