两类最优循环局部修复码的构造

局部修复码是一种能修复多个故障节点的纠删码,在分布式存储系统中被广泛使用,构造最优局部修复码是目前分布式存储编码理论研究的热点问题之一.文章利用有限域Fq上循环码构造了以下两类具有局部修复性(r,δ)的最优局部修复码:1)[3(q+1),3(q+1)-3δ+1,δ+2],其中 q ≡ 1(mod 6),r+δ-1=q+...     

有限域上一类常循环BCH码

本文研究了有限域F_q~2上一类码长为q^2m-1/r(q-1)的常循环BCH码,其中r|(q+1),q是素数幂.首先,给出了该类常循环BCH码是埃尔米特对偶包含码的一个充要条件.其次,确定这类埃尔米特对偶包含常循环BCH码的参数.最后,利用埃尔米特构造,得到了一些参数较好的量子码.     

广义循环Fuzzy矩阵半群的格林关系等价类

研究了广义循环Fuzzy矩阵半群Cn（F）上的格林关系．得到的主要结果是：（1）给出了任意一个o-循环Fuzzy矩阵所在的格林关系各等价类及其基数；（2）给出任意一个，一循环Fuzzy矩阵所在的-等价类及其基数．     

两类循环模糊自动机的弱等价性

定义循环模糊自动机和循环模糊有限状态自动机,并讨论了这两类循环模糊自动机的弱等价性.     

关于两类循环矩阵的非异性

本文分别给出了仅用r-循环矩阵及对称r-循环矩阵的元素本身和参数r,便可做出判断其非异性的五种方法。     

最优(v,{3,4},1,Q)-光正交码的构造

在光纤码分多址(OCDMA)系统中,变重量光正交码被广泛使用,以满足多种服务质量的需求.利用分圆类和斜starter给出了直接构造方法,借助有关循环差阵的递归构造方法,从而构造了两类循环填充设计.通过建立循环填充设计与变重量光正交码之间的联系,证明了当Q∈{{2/3,1/3},{3/4,1/4}}时,最优(v,{3,4},1,Q)-光正交码存在的无穷类.     

具有较少非循环子群共轭类的有限群

设G是有限群,用δ(G)表示群G的非循环子群的共轭类数,πr(G)表示整除|G|的素因子的集合.本文主要研究满足条件δ(G)≤|π(G)|+1的有限群,得到这类群可解,并给出它们的同构分类进一步证明,δ(G)=|π(G)|+2的有限非可解群必同构于A_5或SL(2,5).     

类距离空间中关于循环映射的公共不动点定理

在0-σ-完备的类距离空间中,证明了一类循环压缩映射的公共不动点定理,其中压缩条件包含了二元变距离函数.结果改正并推广了Akram等人最近的结果.     

凸半定规划中关于非奇异性的一个等价条件

本文将给出凸半定规划中关于非奇异性的一个等价条件,它可以看作线性半定规划中非奇异性的等价条件的推广.     

关于分圆域及其最大实子域的类数上界

设ｍ是适合m≠2（ｍｏｄ４）的整数，(?)是ｍ次本原单位根，又设Δ_k,h_m分别是分圆域Ｋ＝Ｑ(?)的判别式和类数．本文证明了：     

On the Distance Distributions of BCH Codes and Their Duals

Based on new bounds on the values of Krawtchoukpolynomials, we improve earlier known estimates forcomponents of the distance distributions of BCH codes and theirduals. Moreover, we show that if one uses estimates on Krawtchoukpolynomials for bounding the error term in the binomial approximationto the distance distribution of BCH codes, the given results are actuallythe best possible. One of the advantages of the proposed approach isthat it provides estimates with no restrictions on the minimumdistance of the code.     

The Automorphism Groups of BCH Codes and of Some Affine-Invariant Codes Over Extension Fields

Affine-invariant codes are extended cyclic codes of length p ^m invariant under the affine-group acting on . This class of codes includes codes of great interest such as extended narrow-sense BCH codes. In recent papers, we classified the automorphism groups of affine-invariant codes berg, bech1. We derive here new results, especially when the alphabet field is an extension field, by expanding our previous tools. In particular we complete our results on BCH codes, giving the automorphism groups of extended narrow-sense BCH codes defined over any extension field.     

The Theory of Cyclic Codes and a Generalization to Additive Codes

We present a new approach to the theory of cyclic and constacyclic codes and generalize the theory to cover the family of additive (not necessarily linear) cyclic codes. The approach is based on the action of the Galois group (cyclotomic cosets). The conventional representation of cyclic codes as ideals in a factor ring of the polynomial ring is not needed.     

The Length of Primitive BCH Codes with Minimal Covering Radius

It is proved that the covering radius of a primitive binary BCH code of length q-1 and designed distance 2t+1, where is exactly 2t-1 (the minimum value possible). The bound for q is significantly lower than the one obtained by O. Moreno and C. J. Moreno [9].     

关于循环阵列码

本文用代数观点来研究循环阵列码,证明了一般的阵列码是一些极小循环阵列码的直和,并且对极小循环阵列码给出了明确的刻画．当有限域的特征不整除群的阶时,给出了直接写出相应的多项式环的本原幂等元的方法,从而可以直接写出所有的极小循环码．     

The Covering Radius of Ternary Cyclic Codes with Length up to 25

The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied. The minimal distances of all codes were recalculated.     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.