Optimal Quaternary Self-Orthogonal Codes of Dimensions Two and Three

The optimal or near optimal quaternary self-orthogonal codes of dimensions 2 and 3 are investigated in this paper,and the relations between the optimal self-orthogonal code length,dimension and the minimum distance are found.By means of constructing the generator matrices of such optimal or near optimal self-orthogonal codes,the optimal codes of dimensions 2 and 3 that achieve the Griesmer bound are determined.Especially,the weight polynomial of the optimal or near optimal quaternary self-orthogonal codes of dimensions 2 is obtained.