Two Classes Of Self-Orthogonal Matrix-Product Codes Over Finite Fields

Matrix-product codes are the products of underlying matrices and input codes,which are constructed by some codes with smaller length.They are the generalization of many famous constructions,such as(a| a b)construction.Self-orthogonal codes are an important class of linear codes,which include Euclidean self-orthogonal codes and Hermitian self-orthogonal codes as subclasses.Self-orthogonal codes over finite fields have rich algebraic structure and various applications in combinatorial design and quantum error-correcting codes.Thus,self-orthogonal codes have received extensive attention.In this dissertation,the constructions of two classes of self-orthogonal matrix-product codes over finte fields are studied.The main contents are as follows.(1)In the case that the underlying matrix is a triangular matrix or an inverse upper triangular matrix,based on nested input codes,an Euclidean self-orthogonal matrix-product code is constructed according to the invertibility of non-singular matrices and the properties of Euclidean self-orthogonal codes.(2)In the case that the underlying matrix or the product of the underlying matrix and its transposition is a double diagonal matrix,an anti-double diagonal matrix,a tridiagonal matrix or an anti-tridiagonal matrix,an Euclidean self-orthogonal matrix-product code is constructed according to the correspondence between Euclidean self-orthogonal codes and their generator matrices and the Euclidean self-orthogonality of input codes.(3)In the case that the underlying matrix is a lower triangular matrix,an inverse upper triangular matrix,a double diagonal matrix,an inverse double diagonal matrix,a tridiagonal matrix or an inverse tridiagonal matrix,and the product of the underlying matrix and its Hermitian transposition is a double diagonal matrix,an inverse double diagonal matrix,a tridiagonal matrix or an inverse tridiagonal matrix,a Hermitian self-orthogonal matrix-product code is constructed according to some properties of nonsingular matrices and Hermitian self-orthogonal codes.(4)Some examples of Euclidean self-orthogonal matrix-product codes and Hermitian self-orthogonal matrix-product codes are given respectively.