This paper gives new methods of constructing symmetric self-dual codes over a finite field GF(q) where q is a power of an odd prime. These methods are motivated by the well-known Pless symmetry codes and quadratic double circulant codes. Using these methods, we construct an amount of symmetric self-dual codes over GF(11), GF(19), and GF(23) of every length less than 42. We also find 153 new self-dual codes up to equivalence: they are [32, 16, 12], [36, 18, 13], and [40, 20, 14] codes over GF(11), [36, 18, 14] and [40, 20, 15] codes over GF(19), and [32, 16, 12], [36, 18, 14], and [40, 20, 15] codes over GF(23). They all have new parameters with respect to self-dual codes. Consequently, we improve bounds on the highest minimum distance of self-dual codes, which have not been significantly updated for almost two decades.

本文给出了在有限域GF ( q ) 上构造对称自对偶码的新方法，其中q是奇素数的幂。这些方法的动机是众所周知的 Pless 对称码和二次双循环码。使用这些方法，我们在长度小于 42 的GF (11)、GF (19) 和GF (23) 上构造了一定数量的对称自对偶码。 我们还找到了 153 个新的自对偶码，直到等价：它们是 [32, 16, 12], [36, 18, 13], 和 [40, 20, 14] GF (11)码，[36, 18, 14] 和 [40, 20, 15] 码GF(19) 和 [32, 16, 12], [36, 18, 14] 和 [40, 20, 15] 代码在GF (23) 上。它们都有关于自对偶码的新参数。因此，我们改进了自对偶码的最高最小距离的界限，近二十年来没有显着更新。