The Research On Self-orthogonal Code Over GF(4)

Coding theory is a specialized branch of the study of information theory. As a very important kind of classical error-correcting code, the study of self-orthogonal code can not only enrich the theoretic and application of the classical error-correcting code, but also can promote the study of quantum error-correct ing codes. This paper referred to the national natural science fund subsidized project (the study of constructing of additive quantum error-correcting and relevant issues), using structural feature of optimal quaternary self-orthogonal codes as studying object, mainly discussed methods of constructing self-orthogonal code and the feature of the optimal quaternary self-orthogonal codes on dimension 3 and 4.The details are as following:1. The constructive methods of quaternary self-orthogonal codes are inferred from that of linear and binary self-orthogonal codes,And then these methods are used to construct some optimal self-orthogonal codes of dimension 4.2. Combination mathematic theory is used to construct the generate matrices of the optimal self-orthogonal codes of dimension 3,at the same time, the weight polynomial of these codes are calculated, and the codes that can reach Griesmer boundary are found.3. The structure of optimal self-orthogonal codes of dimension 4 is researched,and the generate matrices of these codes were constructed, then, the relationship between the optimal or near optimal self-orthogonal codes length and minimal distance were given.4. Each optimal subcode is constructed from the known dual and maximum self-orthogonal codes,and then the optimal code chains are formed.