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1.
本文研究了整数环模16剩余类环Z16上的二次剩余码,讨论了它们的幂等生成元及其扩展码的自对偶性等代数性质,并研究了码长为7的Z16二次剩余码在两种已有的Gray映射下的有趣性质,尤其是确定了它们的Lee重量分布.  相似文献   

2.
Z2k上的二次剩余码   总被引:2,自引:0,他引:2  
Hammons利用Gray映射把一些具有良好纠错能力的非线性码与Z4上的线性码建立了联系.本文进-步对更-般的环上的循环码进行研究,我们定义了Z2k上-类特殊的循环码-二次剩余码,证明了它的存在性及个数,并且证明了它与域上的二次剩余码有类似的性质.  相似文献   

3.
设q为质数幂,m为大于1的正整数,p_(1),p_(2)为不同的奇质数满足gcd(q,p_(1)p_(2))=1且m|gcd(p_(1)-1,p_(2)-1).本文基于m次剩余的思想,给出码长为p_(1)p_(2)的m次剩余码的两种构造.对每种构造,分别给出其为相似文献   

4.
刘宏伟  易风华 《应用数学》2002,15(4):128-133
本文研究了任意有限域Fq上的两个线性码的外积及其有关性质;并给出了由两个线性码构造的外积码的Hamming谱的第1个谱值的界以及最后一个谱值。  相似文献   

5.
2017年詹森构造了6个异基因的8阶二次幻方兼完美幻方,根据它们的特殊性质,创立用一个4阶矩阵代替原有元素的膨胀法,构造出16阶二次幻方兼完美幻方;并对另外2个具有相似性质的8阶二次幻方,也通过膨胀法构造出了16阶二次幻方.  相似文献   

6.
崔杰  裴君莹 《应用数学》2001,14(4):82-87
本文讨论了Z4线性码的支集重量分布,并对类型为4^k1的Z4线性码,给出了联系它与对偶码的支集重量分布之间的广义MacWilliams恒等式。  相似文献   

7.
为实现信号在空间的分集, 关于格的空时分组码的设计近年来备受关注.通过研究与对角的格空时码相关的$\mathbb{Z}[\zeta_{m}]$上的一类二次不可约多项式的判别式$|\Delta|$,确定了$\mathbb{Z}[\zeta_{m}]$上的格空时编码的正规分集乘积的大小.进而, 利用Pell方程的解的性质, 构造性地证明了$m=5, 8, 10, 12$时,$|\Delta|$的值可以任意小. 最后,提出几个关于$\mathbb{Z}[\zeta_{m}]$上的二次不可约和三次不可约多项式的判别式大小的猜想.  相似文献   

8.
刘合国  赵静 《数学学报》2023,(1):187-198
本文从两类整环上的二阶上三角矩阵入手,构造了两个3元生成的亚Abel群,给出了它们的清晰结构,研究了它们的剩余有限性质:一,证明了其中一个无限秩的亚Abel群是剩余有限p-群,这里p是任意素数.二,证明了另一个有限秩的亚Abel群没有这种整齐的剩余有限性质,尽管其结构要简单得多.本文的结果表明,无限可解群里秩的有限性条件对群的剩余有限性具有很大的影响.如何把本文的研究推广到高阶矩阵群,是值得进一步探索的问题.  相似文献   

9.
《中国科学A辑》1996,39(3):193-201
得到了有限域上射影空间中退化Hermite簇上射影码的广义Hamming重量,并计算了它们的广义重量谱.  相似文献   

10.
主要讨论了二次整环的单位、素元、因子分解、二次整环的剩余类环的性质等问题.得到的主要结果有:二次整环的主理想的特征是无限大;当α满足一定条件时,二次整环关于模(α)的剩余类环是无零因子环,其特征为a2-(uaa,bb)+vb2,并且在一定的限制条件下,剩余类环是一个有限域.关键词:  相似文献   

11.
12.
In this paper, we study the residue codes of extremal Type II $\mathbb{Z }_4$ -codes of length 24 and their relations to the famous moonshine vertex operator algebra (VOA). The main result is a complete classification of all residue codes of extremal Type II $\mathbb{Z }_4$ -codes of length 24. Some corresponding results associated to the moonshine VOA are also discussed.  相似文献   

13.
介绍了环sum uiF_2 from i=0 to s-1(us=0)上Typeα和β线性单形码,确定了它们的性质.  相似文献   

14.
The structure of linear codes of constant weight   总被引:1,自引:0,他引:1  
In this paper we determine completely the structure of linear codes over of constant weight. Namely, we determine exactly which modules underlie linear codes of constant weight, and we describe the coordinate functionals involved. The weight functions considered are: Hamming weight, Lee weight, two forms of Euclidean weight, and pre-homogeneous weights. We prove a general uniqueness theorem for virtual linear codes of constant weight. Existence is settled on a case by case basis.

  相似文献   


15.
In this paper, we mainly study the theory of linear codes over the ring \(R =\mathbb {Z}_4+u\mathbb {Z}_4+v\mathbb {Z}_4+uv\mathbb {Z}_4\). By using the Chinese Remainder Theorem, we prove that R is isomorphic to a direct sum of four rings. We define a Gray map \(\Phi \) from \(R^{n}\) to \(\mathbb {Z}_4^{4n}\), which is a distance preserving map. The Gray image of a cyclic code over R is a linear code over \(\mathbb {Z}_4\). We also discuss some properties of MDS codes over R. Furthermore, we study the MacWilliams identities of linear codes over R and give the generator polynomials of cyclic codes over R.  相似文献   

16.
The purpose of this paper is to study codes over finite principal ideal rings. To do this, we begin with codes over finite chain rings as a natural generalization of codes over Galois rings GR(p e l) (including ). We give sufficient conditions on the existence of MDS codes over finite chain rings and on the existence of self-dual codes over finite chain rings. We also construct MDS self-dual codes over Galois rings GF(2 e l) of length n = 2 l for any a ≥ 1 and l ≥ 2. Torsion codes over residue fields of finite chain rings are introduced, and some of their properties are derived. Finally, we describe MDS codes and self-dual codes over finite principal ideal rings by examining codes over their component chain rings, via a generalized Chinese remainder theorem.   相似文献   

17.
Duals of constacyclic codes over a finite local Frobenius non-chain ring of length 4, the length of which is relatively prime to the characteristic of the residue field of the ring are determined. Generators for the dual code are obtained from those of the original constacyclic code. In some cases self-dual codes are determined.  相似文献   

18.
In an earlier paper the authors studied simplex codes of type α and β over and obtained some known binary linear and nonlinear codes as Gray images of these codes. In this correspondence, we study weight distributions of simplex codes of type α and β over The generalized Gray map is then used to construct binary codes. The linear codes meet the Griesmer bound and a few non-linear codes are obtained that meet the Plotkin/Johnson bound. We also give the weight hierarchies of the first order Reed-Muller codes over The above codes are also shown to satisfy the chain condition.A part of this paper is contained in his Ph.D. Thesis from IIT Kanpur, India  相似文献   

19.
In this paper we consider stabilizer codes over local Frobenius rings. Firstly, we study the relative minimum distances of a stabilizer code and its reduction onto the residue field. We show that for various scenarios, a free stabilizer code over the ring does not underperform the according stabilizer code over the field. This leads us to conjecture that the same is true for all free stabilizer codes. Secondly, we focus on the isometries of stabilizer codes. We present some preliminary results and introduce some interesting open problems.  相似文献   

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