10 citations · 31 across the 15 of their papers we have counts for
15 papers
Complete weight enumerators and weight hierarchies for linear codes from quadratic forms
Xiumei Li, Xiaotong Sun, Min Sha
In this paper, for an odd prime power , we extend the construction of Xie et al. \cite{XOYM2023} to propose two classes of linear codes and …
On Euler's totient function of polynomials over finite fields
Xiumei Li, Min Sha
In this paper, we study some typical arithmetic properties of Euler's totient function of polynomials over finite fields. Especially, we study polynomial analogues of some classica…
Weight hierarchies of 3-weight linear codes from two -ary quadratic functions
Xiumei Li, Fei Li
The weight hierarchy of a linear code has been an important research topic in coding theory since Wei's original work in 1991. Choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F…
Weight hierarchies of three-weight -ary linear codes from inhomogeneous quadratic forms
Shupeng Hu, Fei Li, Xiumei Li
The weight distribution and weight hierarchy of a linear code are two important research topics in coding theory. In this paper, choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times…
On the Lucas and Lehmer sequences in Dedekind domains
Xiumei Li, Giulio Peruginelli, Min Sha
In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the…
Weight hierarchies and weight distributions of a familiy of -ary linear codes
Fei Li, Xiumei Li
The weight distribution and weight hierarchy of linear codes are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous…
A proof of Sondow's conjecture on the Smarandache function
Xiumei Li, Min Sha
The Smarandache function of a positive integer , denoted by , is defined to be the smallest positive integer such that divides the factorial . In this note, we…
Polynomial analogue of the Smarandache function
Xiumei Li, Min Sha
In the integer case, the Smarandache function of a positive integer is defined to be the smallest positive integer such that divides the factorial . In this paper,…
Congruence preserving functions in the residue class rings of polynomials over finite fields
Xiumei Li, Min Sha
In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting…
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
Fei Li, Xiumei Li
We restrict a degenerate quadratic form over a finite field of odd characteristic to subspaces. Thus, a quotient space related to is introduced. Then we get a non-degenerat…
Gauss factorials of polynomials over finite fields
Xiumei Li, Min Sha
In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.
Polynomial functions in the residue class rings of Dedekind domains
Xiumei Li, Min Sha
In this paper, as an extension of the integer case, we define polynomial functions over the residue class rings of Dedekind domains, and then we give canonical representations and…
On the elliptic curve over some certain imaginary quadratic fields
Xiumei Li
In this paper, we will talk about the titled elliptic curve defined over imaginary quadratic fields such as , where is congruent to 3 modulo 8 and $(p,q)…
On the Selmer groups and Mordell-Weil groups of elliptic curves over imaginary quadratic number fields of class number one
Xiumei Li
Let and be odd prime numbers with the Selmer groups, Shafarevich-Tate groups ( and part) and their dual ones as well the Mordell-Weil grou…
Factoring integer using elliptic curves over rational number field
Xiumei Li, Jinxiang Zeng
For the integer of the product of two distinct odd primes, we construct an elliptic curve over , where is a parameter dependent on the…