Fei Li

Fei Li
Anhui University of Finance and Economics | AUFE · School of Statistics and Applied Mathematics

PHD

About

17
Publications
882
Reads
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87
Citations
Introduction
Skills and Expertise
Additional affiliations
January 2011 - January 2016
Anhui University of Finance and Economics
Position
  • Researcher
September 2005 - June 2011
Capital Normal University
Position
  • PhD Student

Publications

Publications (17)
Article
Full-text available
The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over Fq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepa...
Article
We restrict quadratic forms to subspaces of finite fields and obtain some interesting results about dual spaces. On this basis, we solve the weight hierarchies of a class of linear codes associated with non-degenerate quadratic forms.
Article
Full-text available
Researchers in the past have studied eigenvalues of Cayley digraphs or graphs. We are interested in characterizing Cayley digraphs on a finite commutative group G whose eigenvalues are algebraic integers in a given number field K. We succeed in finding a method to do so. The number of such Cayley digraphs are computed.
Preprint
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of a linear code has many applications such as on the type II wire-tap channel, dealing with t-resilient functions and trellis or branch complexity of linear codes and so on. In this paper, we present a fo...
Article
Full-text available
In the past decades, linear codes with a few weights have been extensively studied for their applications in space communication, data storage and cryptography etc. We construct several classes of binary linear codes and determine their weight distributions. Most of these codes can be used in secret sharing schemes.
Article
Full-text available
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two alternative formulas to calculate their generalized Hamming weights. Lastly, we determine their weight distribution a...
Article
Weight hierarchies of linear codes have been an interesting topic due to their important values in theory and applications in cryptography. In this paper, we restrict a degenerate quadratic form f over a finite field of odd characteristic to subspaces and introduce a quotient space related to the degenerate quadratic form f. From the polynomial f o...
Article
Linear codes have been an interesting subject of study for many years. In this paper, for an odd prime p, a class of three-weight linear codes over \(\mathbb {F}_{p}\) are constructed and the complete weight enumerators of these linear codes are also settled. These codes have applications in authentication codes, association schemes and data storag...
Article
Full-text available
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three weights.
Article
Full-text available
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight distribution is determined. Results show that they are at most 4-weight linear codes. Additionally, these cod...
Article
Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set. Results show that the codes are at almost seven-weight linear codes and they may have applications in secret sharin...
Article
Full-text available
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, two classes of three-weight linear codes over Fp are constructed. The weight distributions of the linear codes are settled. These codes have applications in...
Article
Recently, linear codes with few weights have been widely studied, since they have applications in data storage systems, communication systems and consumer electronics. In this paper, we present a class of three-weight and five-weight linear codes over Fp, where p is an odd prime and Fp denotes a finite field with p elements. The weight distribution...
Article
A number field K is a finite extension of rational number field Q. A circulant digraph integral over K means that all its eigenvalues are algebraic integers of K. In this paper we give the sufficient and necessary condition for circulant digraphs which are integral over a number field K. And we solve the Conjecture3.3 in [XM] and find it is affirma...
Article
Full-text available
Let $ R \subset \R $ be a GCD-domain. In this paper, Weinberg's conjecture on the $ n \times n $ matrix algebra $ M_{n}(R) \ (n \geq 2) $ is proved. Moreover, all the lattice orders (up to isomorphisms) on a full $ 2 \times 2 $ matrix algebra over $ R $ are obtained.
Article
Full-text available
In this paper, we extend the ideas of Feng [F1], Feng-Xiong [FX] and Faulkner-James [FJ] to calculate the Selmer groups of elliptic curves $ y^{2} = x (x + \varepsilon p D) (x + \epsilon q D). $ Comment: 24
Article
Full-text available
In this paper, we calculate the $ \phi (\hat{\phi})-$Selmer groups $ S^{(\phi)} (E / \Q) $ and $ S^{(\hat{\varphi})} (E^{\prime} / \Q) $ of elliptic curves $ y^{2} = x (x + \epsilon p D) (x + \epsilon q D) $ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be ar...

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Projects

Project (1)
Project
construct linear codes with few weights and dermine their parameters,for example, weight distributions, complete weight enumerator,etc.