The classification of self-orthogonal codes of length 42

Abstract

Self-orthogonal codes play an important role in constructing quantum-error-correcting codes. In this paper, we prove that if quasi-symmetric 2-(41, 9, 9) design exists, then it arises from self-orthogonal and self-complementary [Formula: see text] codes with dual distance of at least 5. Moreover, we emphasize the enumeration of inequivalent doubly-even codes with the needed dual distance and an automorphism of order 7. This is found to be precisely 8.