Classification of circulant and 4-circulant extremal additive self-dual codes

The purpose is to complete the classification of extremal additive circulant self-dual codes of lengths up to 15 and construct some good such codes for lengths 16 ≤ n ≤ 30. We also complete the classification of extremal additive 4-circulant self-dual codes of lengths 4, 6, 8, 12, 14, and 16 and most codes of length 10 and construct good such codes of even lengths up to 22. As a byproduct, we obtained several new extremal self-dual Type I [[16,0,6]] codes, Type II [[22,0,8]] codes, and a Type I [[22,0,8]] code, all with 4-circulant generator matrices.