In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described in Tonchev (J Combinat Theory Ser A 52:197-205, 1989) in order to obtain self-orthogonal codes over an arbitrary field. We extend construction self-orthogonal codes from orbit matrices of self-orthogonal designs and weakly self-orthogonal 1-designs such that block size is odd and block intersection numbers are even described in Crnković (Adv Math Commun 12:607–628, 2018). Also, we generalize mentioned construction in order to obtain self-orthogonal codes over an arbitrary field. We construct weakly self-orthogonal designs invariant under an action of Mathieu group \(M_{11}\) and, from them, binary self-orthogonal codes.

在本文中，我们概括了从Tonchev（J Combinat Theory Ser A 52：197-205，1989）中描述的弱自正交设计中获得的二进制自正交代码的构造，以便在任意字段上获得自正交代码。我们从自正交设计和弱自正交1设计的轨道矩阵扩展构造自正交代码，以使块大小为奇数，甚至在Crnković中描述了块相交数（Adv Math Commun 12：607–628，2018） 。另外，我们对提到的构造进行了概括，以便在任意场上获得自正交码。我们在Mathieu群\（M_ {11} \）的作用下构造弱自正交设计不变式，并从中构造出二进制自正交代码。