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An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.Comment: The title is change

In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even self-dual codes of length 40. * This work was supported by JST PRESTO program.

Several methods for classifying self-orthogonal codes up to equivalence are presented. These methods are used to classify self-orthogonal codes with largest possible minimum distance over the fields F 3 and F 4 for lengths n ≤ 29 and small dimensions (up to 6). Some properties of the classified codes are also presented. In particular, an extensive collection of quantum error-correcting codes is obtained.