A Class Of Linear Codes Based On Matrix Spaces

Let IFq be a finite field with q elements,Fqm×m be the set of all m x m matrices,and Sr={X1,X2,…,Xn} be the set of all m×m symmetric matrices of rank r.Suppose Tr represents the trace of the matrixis,that is,the sum of the diagonal elements of the square matrix,then C(r,m,q)={(Tr(AX1),Tr(AX2),…,Tr(AXn))|A∈Fqm×m}is a subspace of the n-dimensional row vector space Fqn over Fq.Therefore,C(r,m,q)is a q-ary linear code of length n.In this paper,we discusse the properties of linear code C(r,m,q),and give the parameters of linear code C(1,m,q)and C(2,m,q)when q is odd.