Classification of extremal and $s$-extremal binary self-dual codes of length 38

Abstract—In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. The classification of s-extremal [38, 19, 6] codes permits to achieve the classification of all s-extremal codes with d = 6.