Finite projective geometry method is effectively used to study the relative generalized Hamming weights of 4-dimensional linear codes, which are divided into 9 classes in order to get much more information about the r...Finite projective geometry method is effectively used to study the relative generalized Hamming weights of 4-dimensional linear codes, which are divided into 9 classes in order to get much more information about the relative generalized Hamming weights, and part of the relative generalized Hamming weights of a 4-dimensional linear code with a 1-dimensional subcode are determined.展开更多
The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective ...The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.展开更多
C is an [n, k, d]q linear code over Fq. And s（C） = n ＋ 1 - k - d is the Singleton defect of C. An MDS code C with s（C） = 0 has been studied extensively. Recently, a near-MDS code C with s（C） = s（C⊥） = 1 is s...C is an [n, k, d]q linear code over Fq. And s（C） = n ＋ 1 - k - d is the Singleton defect of C. An MDS code C with s（C） = 0 has been studied extensively. Recently, a near-MDS code C with s（C） = s（C⊥） = 1 is studied by many scholars, where C⊥ denotes the dual code of C. This paper concentrates on the linear code C with s（C） = s（C⊥） = 2, and the author calls it an NNMDS code. A series of iff conditions of NNMDS codes are presented. And the author gives an upper bound on length of NNMDS codes. In the last, some examples of NNMDS are given.展开更多
The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a pr...The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes which substantially improves the existing result.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11171366 and 61170257the Special Training Program of Beijing Institute of Technology
文摘Finite projective geometry method is effectively used to study the relative generalized Hamming weights of 4-dimensional linear codes, which are divided into 9 classes in order to get much more information about the relative generalized Hamming weights, and part of the relative generalized Hamming weights of a 4-dimensional linear code with a 1-dimensional subcode are determined.
基金supported by the National Natural Science Foundation of China (Nos. 61303212 and 61170080)the State Key Program of the National Natural Science of China (Nos. 61332019 and U1135004)the Fundamental Research Funds for the Central Universities, South-Central University for Nationalities (No. CZY14019)
文摘The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.
基金supported by Key Disciplines of Shanghai Municipality under Grant No.S30104
文摘C is an [n, k, d]q linear code over Fq. And s（C） = n ＋ 1 - k - d is the Singleton defect of C. An MDS code C with s（C） = 0 has been studied extensively. Recently, a near-MDS code C with s（C） = s（C⊥） = 1 is studied by many scholars, where C⊥ denotes the dual code of C. This paper concentrates on the linear code C with s（C） = s（C⊥） = 2, and the author calls it an NNMDS code. A series of iff conditions of NNMDS codes are presented. And the author gives an upper bound on length of NNMDS codes. In the last, some examples of NNMDS are given.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 60972033 and 60832001.
文摘The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes which substantially improves the existing result.
