Research On Constant Dimensional Codes Based On Singular Pseudo-symplectic Spaces Over Finite Fields

Network coding is an information exchange technology that integrates routing and coding.The traditional random linear network coding is a powerful tool to spread information in the network,however,it is particularly vulnerable to the interference of errors from different sources,such as the noise,malicious or error nodes,insufficient minimum cut sets and so on.Subspace codes,as an important research content of network coding,can check and correct errors.It is widely used in incoherent linear network coding,linear authentication codes and other fields.In the random linear network coding,constant-dimensional subspace codes have an effective way of message transmission,so the research of constant-dimensional subspace codes are also a central theme.The geometric properties of pseudo-symplectic spaces and singular pseudo-symplectic spaces over finite fields are clear,and the combination structure is good.Therefore,the subspaces of pseudo-symplectic space and the subspaces of singular pseudo-symplectic space can be used to construct subspaces codes,respectively.In this paper,we study the basic problem of the performance bounds of the constructed subspace codes.Firstly,we compute the Sphere-packing bound,Singleton bound,Gilbert-Varshamov bound and Wang-Xing-Safavi-Naini bound on the subspace codes(2n+δ,M,d,(m,0,0,0))based on subspaces of type(m,0,0,0)in pseudo-sympletic spaces Fq(2n+δ)and on the subspace codes(2n+δ+l,M,d,(m,0,0,0))based on subspaces of type(m,0,0,0)in singular pseudo-sympletic spaces Fq(2n+δ+l).Secondly,we compute the Sphere-packing bound,Singleton bound,Gilbert-Varshamov bound and Wang-Xing-Safavi-Naini bound on the subspace codes(2n+2,M,d,(m,0,0,1))based on subspaces of type(m,0,0,1)in pseudo-sympletic spaces Fq(2n+2)and on the subspace codes(2n+2+l,M,d,(m,0,0,1))based on subspaces of type(m,0,0,1)in singular pseudo-sympletic spaces Fq(2n+2+l).