Recently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square q, we utilize generalized Reed-Solomon (GRS) codes and their extended codes to provide four generic families of q-ary MDS Euclidean self-dual codes. In particular, for large square q, our constructions take up a proportion of generally more than 34% in all the possible lengths of q-ary MDS Euclidean self-dual codes, which is larger than the previous results. Moreover, two new families of MDS Euclidean self-orthogonal codes and two new families of MDS Euclidean almost self-dual codes are given similarly.

翻译：最近,对新的MDS Euclidean自体法典的构建进行了广泛调查,在本文中,对于正方q,我们使用通用Reed-Solomon(GRS)法典及其扩展法典来提供四套Q-ary MDS Euclidean自体法典的通用家族。特别是对于大方q,我们的建筑在q-ary MDS Euclidean自体法典的所有可能长度中所占的比例一般超过34%,这比以前的结果要大。此外,对MDS Euclidean自体法典的两个新家族和MDS Euclidean几乎自体法典的两个新家族也作了类似的介绍。