Constructions Of Several Classes Of Subspace Codes

In recent years,the application of subspace codes in random network coding has received widespread attention,especially,the application of constant dimension subspace codes.There are many people working on constructing constant dimension subspace codes with size and minimum distance as large as possible.Especially,they are keen to find optimal cyclic constant dimension subspace codes.In recent papers,Ben-Sasson et al.and Otal and Ozbudak have successively constructed optimal cyclic constant dimension subspace codes using subspace polynomials,and they have obtained larger codes when the minimum distance remains the same by combining codes.Based on these works,Bocong Chen and Hongwei Liu have given a method for constructing optimal codes using more general subspace trinomials.Recently,some scholars have further studied the properties and applications of subspace codes.In this paper,we continue to study the structure of general cyclic constant dimensional subspace codes,and we obtain some new results.By generalizing these results,we explore the ideas of computing the size and minimum distance of codes constructed by arbitrary subspace trinomials in Chapter three.Based on the obtained results,we generalize some other results in the above articles.In Chapter four,we study the size and minimum distance of cyclic constant dimension subspace codes constructed by subspace polynomials obtained by combining two subspace polynomials.Based on these works,we give some cyclic constant dimension subspace codes with size and minimum distance as large as possible.In particular,we construct a class of subspace codes by subspace quadrinomials obtained by combining two sub-space binomials.We obtain larger subspace codes by combining codes construct by some combined subspace quadrinomials.