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Xiumei Li

Publications and source records attributed to Xiumei Li.

At least 19 recordsLinked to original sources
arXiv2026

TAFA-GSGC: Group-wise Scalable Point Cloud Geometry Compression with Progressive Residual Refinement

Scalable compression is essential for bandwidth-adaptive transmission, yet most learned codecs are optimized for a fixed rate-distortion point, making rate adaptation costly due to re-encoding or maintaining multiple bitstreams. In this work, we propose TAFA-GSGC, a scalable learned point cloud geometry codec that enables multi-quality decoding from a single bitstream and a single trained model. TAFA-GSGC combines layered residual refinement with channel-group entropy coding, and introduces a Target-Aligned Feature Aggregation module to reduce cross-layer redundancy in enhancement residuals. Our framework supports up to 9 decodable quality levels with monotonic quality improvement as more subbitstreams are received, while maintaining strong compression efficiency. Compared with the PCGCv2 baseline, TAFA-GSGC demonstrates improved RD performance, achieving average BD-rate reductions of 4.99% and 5.92% in terms of D1-PSNR and D2-PSNR, respectively.

cs.CV↗
arXiv2025

Complete weight enumerators and weight hierarchies for linear codes from quadratic forms

In this paper, for an odd prime power $q$, we extend the construction of Xie et al. \cite{XOYM2023} to propose two classes of linear codes $\mathcal{C}_{Q}$ and $\mathcal{C}_{Q}'$ over the finite field $\mathbb{F}_{q}$ with at most four nonzero weights. These codes are derived from quadratic forms through a bivariate construction. We completely determine their complete weight enumerators and weight hierarchies by employing exponential sums. Most of these codes are minimal and some are optimal in the sense that they meet the Griesmer bound. Furthermore, we also establish the weight hierarchies of $\mathcal{C}_{Q,N}$ and $\mathcal{C}_{Q,N}'$, which are the descended codes of $\mathcal{C}_{Q}$ and $\mathcal{C}_{Q}'$.

cs.IT↗
arXiv2025

Optimized Learned Image Compression for Facial Expression Recognition

Efficient data compression is crucial for the storage and transmission of visual data. However, in facial expression recognition (FER) tasks, lossy compression often leads to feature degradation and reduced accuracy. To address these challenges, this study proposes an end-to-end model designed to preserve critical features and enhance both compression and recognition performance. A custom loss function is introduced to optimize the model, tailored to balance compression and recognition performance effectively. This study also examines the influence of varying loss term weights on this balance. Experimental results indicate that fine-tuning the compression model alone improves classification accuracy by 0.71% and compression efficiency by 49.32%, while joint optimization achieves significant gains of 4.04% in accuracy and 89.12% in efficiency. Moreover, the findings demonstrate that the jointly optimized classification model maintains high accuracy on both compressed and uncompressed data, while the compression model reliably preserves image details, even at high compression rates.

cs.CV↗
arXiv2024

Some three-weight linear codes and their complete weight enumerators and weight hierarchies

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic functions via a bivariate construction and then determine the complete weight enumerators and weight hierarchies of these linear codes completely. This paper generalizes some results in Li et al. (2022) and Hu et al. (2024).

cs.IT↗
arXiv2024

On Euler's totient function of polynomials over finite fields

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 classical conjectures about Euler's totient function, such as Carmichael's conjecture, Sierpi\'{n}ski's conjecture, and Erd\"{o}s' conjecture.

math.NT↗
arXiv2023

PIPO-Net: A Penalty-based Independent Parameters Optimization Deep Unfolding Network

Compressive sensing (CS) has been widely applied in signal and image processing fields. Traditional CS reconstruction algorithms have a complete theoretical foundation but suffer from the high computational complexity, while fashionable deep network-based methods can achieve high-accuracy reconstruction of CS but are short of interpretability. These facts motivate us to develop a deep unfolding network named the penalty-based independent parameters optimization network (PIPO-Net) to combine the merits of the above mentioned two kinds of CS methods. Each module of PIPO-Net can be viewed separately as an optimization problem with respective penalty function. The main characteristic of PIPO-Net is that, in each round of training, the learnable parameters in one module are updated independently from those of other modules. This makes the network more flexible to find the optimal solutions of the corresponding problems. Moreover, the mean-subtraction sampling and the high-frequency complementary blocks are developed to improve the performance of PIPO-Net. Experiments on reconstructing CS images demonstrate the effectiveness of the proposed PIPO-Net.

eess.SP↗
arXiv2023

Weight hierarchies of 3-weight linear codes from two $p$-ary quadratic functions

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_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+g(y)=0\Big\}$ as a defining set , where $f(x),g(y)$ are quadratic forms over $\mathbb{F}_{p^{s_i}},i=1,2$, respectively, with values in $\F_p$, we construct a family of 3-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies completely. Most of the codes can be used in secret sharing schemes.

cs.IT↗
arXiv2023

Weight hierarchies of three-weight $p$-ary linear codes from inhomogeneous quadratic forms

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\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+\Tr_1^{s_2}(\alpha y)=0\Big\}$ as a defining set , where $\alpha\in\mathbb{F}_{p^{s_2}}^*$ and $f(x)$ is a quadratic form over $\mathbb{F}_{p^{s_1}}$ with values in $\F_p$, whether $f(x)$ is non-degenerate or not, we construct a family of three-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.

cs.IT↗
arXiv2020

On the Lucas and Lehmer sequences in Dedekind domains

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 primitive divisor results for such sequences in function fields.

math.NT↗
arXiv2020

Weight hierarchies and weight distributions of a familiy of $p$-ary linear codes

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 quadratic functions over $\mathbb{F}_{q}^{2},$ we construct a family of $3$-weight $p$-ary linear codes and determine their weight distributions and weight hierarchies. Most of the codes can be used in secret sharing schemes.

cs.IT↗
arXiv2020

Weight distributions of several families of 3-weight binary linear codes

The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the exponential sum $\sum_{x\in \mathbb{F}_{2^{e}}}\chi_1\left(ax^{2^{\alpha}+1}+bx\right).$ Then, using the above exponential sum, we construct several families of binary linear codes of $3$-weight and determine their weight distributions. Moreover, Most of them can be used in secret sharing schemes.

cs.IT↗
arXiv2020

Weight distributions and weight hierarchies of two classes of binary linear codes

Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes 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 first present a formula for computing the weight hierarchies of linear codes constructed by the generalized method of defining sets. Then, we construct two classes of binary linear codes with a few weights and determine their weight distributions and weight hierarchies completely. Some codes of them can be used in secret sharing schemes.

cs.IT↗
arXiv2019

A proof of Sondow's conjecture on the Smarandache function

The Smarandache function of a positive integer $n$, denoted by $S(n)$, is defined to be the smallest positive integer $j$ such that $n$ divides the factorial $j!$. In this note, we prove that for any fixed number $k > 1$, the inequality $n^k < S(n)!$ holds for almost all positive integers $n$. This confirms Sondow's conjecture which asserts that the inequality $n^2 < S(n)!$ holds for almost all positive integers $n$.

math.NT↗
arXiv2019

Polynomial analogue of the Smarandache function

In the integer case, the Smarandache function of a positive integer $n$ is defined to be the smallest positive integer $k$ such that $n$ divides the factorial $k!$. In this paper, we first define a natural order for polynomials in $\mathbb{F}_q[t]$ over a finite field $\mathbb{F}_q$ and then define the Smarandache function of a non-zero polynomial $f \in \mathbb{F}_q[t]$, denoted by $S(f)$, to be the smallest polynomial $g$ such that $f$ divides the Carlitz factorial of $g$. In particular, we establish an analogue of a problem of Erd{\H o}s, which implies that for almost all polynomials $f$, $S(f)=t^d$, where $d$ is the maximal degree of the irreducible factors of $f$.

math.NT↗
arXiv2018

Congruence preserving functions in the residue class rings of polynomials over finite fields

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 formula for such congruence preserving functions, determine a necessary and sufficient condition under which all congruence preserving functions are also polynomial functions, and characterize such functions.

math.NT↗
arXiv2018

Weight hierarchies of a family of linear codes associated with degenerate quadratic forms

We restrict a degenerate quadratic form $f$ over a finite field of odd characteristic to subspaces. Thus, a quotient space related to $f$ is introduced. Then we get a non-degenerate quadratic form induced by $f$ over the quotient space. Some related results on the subspaces and quotient space are obtained. Based on this, we solve the weight hierarchies of a family of linear codes related to $f.$

cs.IT↗
arXiv2017

Polynomial functions in the residue class rings of Dedekind domains

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 counting formulas for such polynomial functions. In particular, we give an explicit formula for the number of polynomial functions over the residue class rings of polynomials over finite fields.

math.NT↗