The generalized Hamming weights and generalized weight spectra of the protective codes from degenerate Hermitian varieties in projective spaces over finite fields are determined.
Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goet...Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goethals codes and their dual codes are proved to be cyclic.展开更多
We derive a lower bound of the generalized Hamming weights of the codes over affine varieties , which are defined by appropriate sequences of rational polynomials over varieties.
当 A是特殊的 (n,1,n)等重码和 (n,n,1)等重等距码时 ,通过对两个旧码 A和 B构造一个新码 A B即直和码的分析 ,给出了 A B广义 Ham ming重量与 A、B的广义 Ham ming重量的关系 ;在 A、B是一般情形下 ,对直和码的广义 Ham ming重量进行...当 A是特殊的 (n,1,n)等重码和 (n,n,1)等重等距码时 ,通过对两个旧码 A和 B构造一个新码 A B即直和码的分析 ,给出了 A B广义 Ham ming重量与 A、B的广义 Ham ming重量的关系 ;在 A、B是一般情形下 ,对直和码的广义 Ham ming重量进行了研究。展开更多
文摘The generalized Hamming weights and generalized weight spectra of the protective codes from degenerate Hermitian varieties in projective spaces over finite fields are determined.
文摘Some properties such as type, trace description, symmetrized weight enumerator, and generalizedHamming weights of the dual of quaternary Goethals codes are discussed. Furthermore, the shortened codesof quaternary Goethals codes and their dual codes are proved to be cyclic.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.19701033).
文摘We derive a lower bound of the generalized Hamming weights of the codes over affine varieties , which are defined by appropriate sequences of rational polynomials over varieties.
