共查询到19条相似文献,搜索用时 187 毫秒
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.
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.
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.
徐向东 《数学的实践与认识》2021,(5):278-284
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.
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.
8.
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
9.
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
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.
Ping Li Xuemei Guo Shixin Zhu Xiaoshan Kai 《Journal of Applied Mathematics and Computing》2017,54(1-2):307-324
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
14.
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
15.
Nuh Aydin Yasemin Cengellenmis Abdullah Dertli 《Designs, Codes and Cryptography》2018,86(6):1249-1255
In this paper, we study \(\lambda \)-constacyclic codes over the ring \(R=\mathbb {Z}_4+u\mathbb {Z}_4\) where \(u^{2}=1\), for \(\lambda =3+2u\) and \(2+3u\). Two new Gray maps from R to \(\mathbb {Z}_4^{3}\) are defined with the goal of obtaining new linear codes over \(\mathbb {Z}_4\). The Gray images of \(\lambda \)-constacyclic codes over R are determined. We then conducted a computer search and obtained many \(\lambda \)-constacyclic codes over R whose \(\mathbb {Z}_4\)-images have better parameters than currently best-known linear codes over \(\mathbb {Z}_4\). 相似文献
16.
The structure of linear codes of constant weight 总被引:1,自引:0,他引:1
Jay A. Wood 《Transactions of the American Mathematical Society》2002,354(3):1007-1026
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.
17.
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
18.
C.A. Castillo-Guillén C. Rentería-Márquez H. Tapia-Recillas 《Discrete Mathematics》2018,341(4):919-933
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
19.
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