Construction of extremal self-dual codes over [formula omitted] with an automorphism of odd order

Abstract

We complete the classification the Lee-extremal self-dual codes over the ring F2+uF2 of lengths 21 and 22 with a nontrivial automorphism of odd prime order except the case for an automorphism of order 3 with seven cycles, and we partially classify the exceptional case. In particular, we show that there are 138 (respectively, 6723) inequivalent Lee-extremal self-dual codes of length 21 (respectively, 22) with an automorphism of odd prime order. We use the decomposition theory for self-dual codes over F2+uF2 with an automorphism of odd prime order as the same approaches made by Huffman. And we also use an extension method as a new approach, and the current approach is extending the even subcode part while the fixed subcode part is extended in the authorsʼ previous work.