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Computer Science, Theory & Methods
Jian Gao, Xiangrui Meng, Fang-Wei Fu
Summary: This paper determines the weight distribution of several classes of double cyclic codes over Galois rings using Gauss sums.
DESIGNS CODES AND CRYPTOGRAPHY
(2022)
Article
Computer Science, Theory & Methods
Youcef Maouche
Summary: In this paper, the symbol-pair weight distribution of irreducible cyclic codes is studied. Generalized cyclotomic numbers are defined and their properties are provided. By using a character sum, a relationship between the symbol-pair weight of irreducible cyclic codes, generalized cyclotomic numbers, and Gaussian periods is established. Moreover, the symbol-pair weight distribution of certain classes of irreducible cyclic codes is determined.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2023)
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Computer Science, Theory & Methods
Xiangrui Meng, Jian Gao, Fang-Wei Fu, Fanghui Ma
Summary: In this study, the Hamming weight distribution of Q2DC codes is determined using the trace representation and Gauss sums, and some classes of Q2DC codes satisfying certain conditions are constructed.
DESIGNS CODES AND CRYPTOGRAPHY
(2023)
Article
Mathematics, Applied
Xi Liu
Summary: This paper calculates several identities involving Gauss sums of the 2(k)-order character modulo an odd prime p using elementary and analytic methods, and finally provides several exact and interesting formulas for them. The properties of classical Gauss sums play a crucial role in the proof presented in this paper.
Article
Quantum Science & Technology
Yanqing Dai, Xiusheng Liu
Summary: This paper proposes two new methods for constructing QSCs and provides concrete examples. These methods can effectively correct the effects of quantum noise on qubits and misalignment in block synchronization.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Mathematics, Applied
Shudi Yang, Zheng-An Yao
Summary: A class of projective binary linear codes with at most three nonzero weights are constructed and their weight distributions are investigated using Weil sums. Some of these codes contain optimal codes, and their dual codes are also studied, with some being optimal or almost optimal.
Article
Mathematics
Jiafan Zhang, Yuanyuan Meng
Summary: This paper utilizes the elementary methods and properties of classical Gauss sums to study the calculation problems of mean values of character sums of special polynomials and derives several interesting calculation formulae. Furthermore, a criterion is provided for determining whether 2 is a cubic residue for any odd prime p.
Article
Mathematics, Applied
Zhiyong Zheng, Ziwei Hong
Summary: In this paper, new bounds for polynomial character sums are shown by utilizing polynomial Gauss sums and a formula from L. Carlitz on exponential sums over function fields. The method presented is elementary and independent of the well-known result on the L-function associated with algebraic curves over finite fields by A. Weil.
JOURNAL OF MATHEMATICAL INEQUALITIES
(2021)
Article
Mathematics
Ayesha Hussain
Summary: In this paper, we investigate the distribution of continuous paths of Dirichlet character sums modulo prime q on the complex plane. We find the limiting distribution as q approaches infinity by using Steinhaus random multiplicative functions and state properties of this random process. This study is motivated by the work of Kowalski and Sawin on Kloosterman paths.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2022)
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Computer Science, Hardware & Architecture
Xina Zhang, Xiaoni Du, Rong Wang, Fujun Zhang
Summary: This paper presents a class of five-weight linear codes over odd prime field, which have various applications in different fields and are close to being optimal in some aspects.
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
(2021)
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Computer Science, Theory & Methods
Varsha Chauhan, Anuradha Sharma, Sandeep Sharma, Monika Yadav
Summary: This paper investigates the Hamming weights and weight distributions of multi-twisted codes, identifying optimal equidistant linear codes with connections to combinatorial designs and other useful minimal linear codes. Illustrative examples and listings of various linear codes are provided for further understanding.
DESIGNS CODES AND CRYPTOGRAPHY
(2021)
Article
Mathematics, Applied
Wenpeng Zhang, Xiaodan Yuan
Summary: In this paper, the analytical methods and properties of classical Gauss sums are used to study the calculating problems of some Gauss sums involving the character of order 12 modulo an odd prime p, resulting in several new and interesting identities.
Article
Mathematics
Lingyong Ma, Guanjun Li, Fengyan Liu
Summary: This paper focuses on linear codes with few weights and constructs more 3-weight linear codes using ternary near-bent and 2-plateaued functions or r-ary functions, where r is a prime. The weight distributions of the resulting linear codes are determined using some exponential sums.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Sen Wang, Yi Ouyang, Xianhong Xie
Summary: In previous study, optimal codes with few weights were constructed by defining sets on specific rings. This research presents a unified approach for constructing these codes on a general algebra. By applying this approach to a specific case, new classes of linear codes are generated, and their weight enumerators are determined. It is also shown that these codes are either optimal or distance optimal to the Griesmer bound.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics, Applied
Yunfei Su, Xiaoshan Kai
Summary: Cyclic codes with two zeros and length n=q(m-1)/r are explored in this study. A necessary and sufficient condition with minimum distance two is provided for such cyclic codes. It is proven that these cyclic codes have a minimum distance of at most three when q>2r+1. An optimal family of cyclic codes with parameters [2(q(m)-1)/q-1, 2(q(m)- 1)/ q-1 - 2m, 4] is obtained for the case of r=q-1/2.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
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Computer Science, Theory & Methods
Chengju Li, Qin Yue, Ziling Heng
ADVANCES IN MATHEMATICS OF COMMUNICATIONS
(2015)
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Computer Science, Theory & Methods
Chengju Li, Qin Yue, Fang-Wei Fu
DESIGNS CODES AND CRYPTOGRAPHY
(2016)
Article
Computer Science, Theory & Methods
Chengju Li, Sunghan Bae, Jaehyun Ahn, Shudi Yang, Zheng-An Yao
DESIGNS CODES AND CRYPTOGRAPHY
(2016)
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Mathematics
Sunghan Bae, Chengju Li, Qin Yue
DISCRETE MATHEMATICS
(2015)
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Mathematics, Applied
Chengju Li, Qin Yue
FINITE FIELDS AND THEIR APPLICATIONS
(2015)
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Mathematics, Applied
Fengwei Li, Qin Yue, Chengju Li
FINITE FIELDS AND THEIR APPLICATIONS
(2015)
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Computer Science, Interdisciplinary Applications
Chengju Li, Qin Yue, Fang-Wei Fu
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
(2017)
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Computer Science, Theory & Methods
Jaehyun Ahn, Dongseok Ka, Chengju Li
DESIGNS CODES AND CRYPTOGRAPHY
(2017)
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Mathematics
Ziling Heng, Qin Yue, Chengju Li
DISCRETE MATHEMATICS
(2016)
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Computer Science, Theory & Methods
Chengju Li, Sunghan Bae, Haode Yan
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2017)
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Mathematics, Applied
Sunghan Bae, Pyung-Lyun Kang, Chengju Li
FINITE FIELDS AND THEIR APPLICATIONS
(2017)
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Computer Science, Information Systems
Shuxing Li, Chengju Li, Cunsheng Ding, Hao Liu
IEEE TRANSACTIONS ON INFORMATION THEORY
(2017)
Article
Computer Science, Information Systems
Chengju Li, Cunsheng Ding, Shuxing Li
IEEE TRANSACTIONS ON INFORMATION THEORY
(2017)
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Mathematics
Cunsheng Ding, Chengju Li
DISCRETE MATHEMATICS
(2017)
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Mathematics
Hao Liu, Cunsheng Ding, Chengju Li
DISCRETE MATHEMATICS
(2017)
Article
Mathematics, Applied
Li Xu, Cuiling Fan, Dongchun Han
Summary: This paper investigates near maximum distance separable (NMDS) codes with dimension 3. By adding projective points in specific projective geometries, a new class of NMDS codes is obtained, and their properties are studied.
FINITE FIELDS AND THEIR APPLICATIONS
(2024)
Article
Mathematics, Applied
Shiang Tang
Summary: In this paper, we provide new instances of the inverse Galois problem over global function fields for finite groups of Lie type. This is achieved by constructing compatible systems of tadic Galois representations valued in a semisimple group G using Galois theoretic and automorphic methods, and then proving that the Galois images are maximal for a set of primes of positive density based on Larsen's classical result on Galois images for compatible systems.
FINITE FIELDS AND THEIR APPLICATIONS
(2024)
Article
Mathematics, Applied
Huan Sun, Qin Yue, Xue Jia
Summary: In this article, the authors study a family of APN hexanomials F3 that satisfy a certain technical condition. They determine the number of APN hexanomials F3 and provide a theorem for their determination when i = 1. Additionally, they construct a family of APN functions in bivariate form and prove its CCZ-equivalence to F3.
FINITE FIELDS AND THEIR APPLICATIONS
(2024)
Article
Mathematics, Applied
Chandan Kumar Vishwakarma, Rajesh P. Singh
Summary: In this paper, we investigate certain classes of complete permutation polynomials with specific forms and propose methods for constructing PPs and CPPs over finite fields using the AGW criterion. Additionally, we obtain constructions of sets of Mutually orthogonal Latin squares using permutation polynomials over finite fields.
FINITE FIELDS AND THEIR APPLICATIONS
(2024)
Article
Mathematics, Applied
Monika Bishnoi, Pankaj Kumar
Summary: In this paper, we investigate cubic primitive irreducible cyclic codes and provide bounds on their minimum distances. We also demonstrate a connection between solutions of Diophantine equations and weight enumerators of these codes.
FINITE FIELDS AND THEIR APPLICATIONS
(2024)
