期刊：
Linear Algebra and its Applications,2018年553:292-306 ISSN：0024-3795
通讯作者：
Deng, Guodong
作者机构：
[Fan, Yun; Deng, Guodong] China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.;[Fan, Yun; Deng, Guodong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Deng, Guodong] C;China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
If every element of a matrix group is similar to a permutation matrix, then it is called a permutation-like matrix group. References [3], [4] and [5] showed that, if a permutation like matrix group contains a maximal cycle such that the maximal cycle generates a normal subgroup and the length of the maximal cycle equals a prime, or a square of a prime, or a power of an odd prime, then the permutation-like matrix group is similar to a permutation matrix group. In this paper, we prove that if a permutation-like matrix group contains a maximal cycle such that the maximal cycle generates a normal subgroup and the length of the maximal cycle equals any power of 2, then it is similar to a permutation matrix group. (C) 2018 Published by Elsevier Inc.
摘要：
Double circulant matrices are introduced and studied. By a matrix-theoretic method, the rank r of a double circulant matrix is computed, and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a generalization, multiple circulant matrices are also introduced. Two questions on square double circulant matrices are posed.
作者机构：
[Dinh, Hai Q.] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam.;[Dinh, Hai Q.] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam.;[Dinh, Hai Q.] Kent State Univ, Dept Math Sci, 4314 Mahoning Ave, Warren, OH 44483 USA.;[Liu, Hualu; Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Liu, Hualu; Liu, Xiusheng] Hubei Polytech Univ, Sch Math & Phys, Huangshi 435003, Hubei, Peoples R China.
通讯机构：
[Liu, Hualu] H;Hubei Polytech Univ, Sch Math & Phys, Huangshi 435003, Hubei, Peoples R China.
关键词：
Cyclic codes;Constacyclic codes;Self-dual codes;Repeated-root codes;Codes over rings
摘要：
The aim of this paper is to establish all self-dual lambda-constacyclic codes of length p(s) over the finite commutative chain ring R = F-p(m) + uF(p)(m), where p is a prime and u(2) = 0. If lambda = alpha+u beta for nonzero elements alpha, beta of F-p(m), the ideal < u > is the unique self-dual (alpha +u beta)-constacyclic codes. If lambda = gamma for some nonzero element gamma of F-p(m) we consider two cases of gamma. When gamma = gamma(-1), i.e., gamma = 1 or -1, we first obtain the dual of every cyclic code, a formula for the number of those cyclic codes and identify all self-dual cyclic codes. Then we use the ring isomorphism phi to carry over the results about cyclic accordingly to negacyclic codes. When gamma not equal gamma(-1), it is shown that < u > is the unique self-dual gamma-constacyclic code. Among other results, the number of each type of self-dual constacyclic code is obtained. (C) 2017 Elsevier B.V. All rights reserved.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2018年86(9):2091-2113 ISSN：0925-1022
通讯作者：
Xu, Bangteng
作者机构：
[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
期刊：
Designs, Codes, and Cryptography,2017年84(3):473-492 ISSN：0925-1022
通讯作者：
Fan, Yun
作者机构：
[Zhang, Liang; Fan, Yun] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
通讯机构：
[Fan, Yun] C;Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.
关键词：
12E20;94B60;Constacyclic code;Galois inner product;Galois self-dual code;Isometry;q-Coset function
摘要：
Generalizing the Euclidean inner product and the Hermitian inner product, we introduce Galois inner products, and study Galois self-dual constacyclic codes in a very general setting by a uniform method. The conditions for existence of Galois self-dual and isometrically Galois self-dual constacyclic codes are obtained. As consequences, results on self-dual, iso-dual and Hermitian self-dual constacyclic codes are derived.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2017年82(3):543-558 ISSN：0925-1022
通讯作者：
Xu, Bangteng
作者机构：
[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
关键词：
Bent functions;Fourier transforms on G-sets;G-dual sets;G-linear functions;Group actions;Perfect nonlinear functions
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2017年85(2):319-341 ISSN：0925-1022
通讯作者：
Xu, Bangteng
作者机构：
[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Xu, Bangteng] Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
通讯机构：
[Xu, Bangteng] E;Eastern Kentucky Univ, Dept Math & Stat, Richmond, KY 40475 USA.
期刊：
IEEE Transactions on Information Theory,2015年61(1):82-90 ISSN：0018-9448
通讯作者：
Fan, Yun
作者机构：
[Fan, Yun; Lin, Liren] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Fan, Yun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Random quasi-abelian code;threshold;GVbound;balanced code;cumulative weight enumerator
摘要：
For a q-ary random quasi-Abelian code with fixed coindex and constant rate r, it is shown that the Gilbert-Varshamov (GV)-bound is a threshold point: if r is less than the GV-bound at δ ∈ (0, 1 - q
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup>
), then the probability of the relative distance of the random code being greater than δ approaches 1 as the index goes to infinity; whereas, if r is bigger than the GV-bound at δ, then the probability approaches 0. As a corollary, there exist numerous asymptotically good quasi-Abelian codes attaining the GV-bound.
期刊：
IEEE Transactions on Information Theory,2015年61(9):4895-4904 ISSN：0018-9448
通讯作者：
Chen, Bocong
作者机构：
[Chen, Bocong; Ling, San] Nanyang Technol Univ, Sch Phys & Math Sci, Singapore 637616, Singapore.;[Dinh, Hai Q.] Kent State Univ, Dept Math Sci, Warren, OH 44483 USA.;[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Advances in Mathematics,2015年282:265-290 ISSN：0001-8708
通讯作者：
Jin, Ping
作者机构：
[Jin, Ping] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China.;[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Jin, Ping] S;Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China.
摘要：
Let G be a finite group and let F be a finite field of characteristic 2. We introduce F-special subgroups and F-special elements of G. In the case where F contains a pth primitive root of unity for each odd prime p dividing the order of G (e.g. it is the case once F is a splitting field for all subgroups of G), the F-special elements of G coincide with real elements of odd order. We prove that a symmetric FG-module V is metabolic if and only if the restriction VD of V to every F-special subgroup D of G is metabolic, and also, if and only if the characteristic polynomial on V defined by every F-special element of G is a square of a polynomial over F. Some immediate applications to characters, self-dual codes and Witt groups are given. (C) 2015 Elsevier Inc. All rights reserved.
期刊：
Finite Fields and Their Applications,2014年29:247-267 ISSN：1071-5797
通讯作者：
Liu, Hongwei
作者机构：
[Liu, Hongwei; Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ling, San] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637616, Singapore.
通讯机构：
[Liu, Hongwei] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Finite principal ideal ring;Homogeneous weight;Matrix product code
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2014年71(2):201-227 ISSN：0925-1022
通讯作者：
Liu, Hongwei
作者机构：
[Liu, Hongwei; Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Ling, San] Nanyang Technol Univ, Sch Phys Math Sci, Div Math Sci, Singapore 637616, Singapore.
通讯机构：
[Liu, Hongwei] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Linear Algebra and its Applications,2014年450:44-55 ISSN：0024-3795
通讯作者：
Fan, Yun
作者机构：
[Fan, Yun; Deng, Guodong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Fan, Yun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Matrix group;Matrix similarity;Permutation-like group;Permutation matrix group
摘要：
A matrix group is said to be permutation-like if any matrix of the group is similar to a permutation matrix. G. Cigler proved that, if a permutation-like matrix group contains a normal cyclic subgroup which is generated by a maximal cycle and the matrix dimension is a prime, then the group is similar to a permutation matrix group. This paper extends the result to the case where the matrix dimension is a square of a prime. (C) 2014 Elsevier Inc. All rights reserved.
摘要：
Let G be a finite group. A subgroup H of G is called a 2-maximal subgroup of G if there exists a maximal subgroup M of G such that H is a maximal subgroup of M. In this paper, we discuss the influence of π-quasinormality of 2-maximal subgroups of Sylow subgroups on the structure of a finite group, and obtain some sufficient conditions under which the finite group is p-nilpotent, supersolvable, or possesses an ordered Sylow tower.
作者机构：
[Shen, Jing] Naval Univ Engn, Sch Sci, Wuhan 430033, Hubei, Peoples R China.;[Fan, Yun] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
会议名称：
IEEE 5th International Conference on Advanced Computational Intelligence (ICACI)
会议时间：
OCT 18-20, 2012
会议地点：
Nanjing, PEOPLES R CHINA
会议主办单位：
[Shen, Jing] Naval Univ Engn, Sch Sci, Wuhan 430033, Hubei, Peoples R China.^[Fan, Yun] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China.
会议论文集名称：
2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI)
摘要：
This paper exhibits a distinguishing algorithmic feature of a phase transition point of a random system I of m linear equations over a finite field with n variables: the complexity of Gaussian elimination for testing satisfiability of the systems approaches maximum at the satisfiability threshold point m/n = 1, and the worst instances should be found at the point. It is very interesting that the algorithm exactly undergoes an easy/hard transition at the satisfiability threshold point.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2012年62(1):19-29 ISSN：0925-1022
通讯作者：
Zhang, Guanghui
作者机构：
[Fan, Yun; Zhang, Guanghui] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China.;[Zhang, Guanghui] Luoyang Normal Univ, Dept Math, Luoyang 471022, Peoples R China.
通讯机构：
[Zhang, Guanghui] L;Luoyang Normal Univ, Dept Math, Luoyang 471022, Peoples R China.
关键词：
Group code;Permutation code;Self-dual code;Self-dual module;Extension degree
摘要：
Motivated by a research on self-dual extended group codes, we consider permutation codes obtained from submodules of a permutation module of a finite group of odd order over a finite field, and demonstrate that the condition "the extension degree of the finite field extended by n'th roots of unity is odd" is sufficient but not necessary for the existence of self-dual extended transitive permutation codes of length n + 1. It exhibits that the permutation code is a proper generalization of the group code, and has more delicate structure than the group code. Motivated by a research on self-dual extended group codes, we consider permutation codes obtained from submodules of a permutation module of a finite group of odd order over a finite field, and demonstrate that the condition "the extension degree of the finite field extended by n'th roots of unity is odd" is sufficient but not necessary for the existence of self-dual extended transitive permutation codes of length n + 1. It exhibits that the permutation code is a proper generalization of the group code, and has more delicate structure than the group code.
