Double circulant self-dual codes over GF(5)

All distinct double circulant self-dual codes over GF(5), with a minimum weight which is highest among all double circulant self-dual codes, have been found for each length n ≤ 24. For lengths 14, 16 and 20, these codes are extremal. In this paper, we characterize these extremal double circulant self-dual codes. In particular, a classification of extremal double circulant self-dual codes of length 14 is given. We present other double circulant codes which improve the lower bounds on the highest possible minimum weight. A classification of double circulant self-dual codes with parameters [18, 9, 7] and [24, 12, 9] is also given.