共查询到19条相似文献,搜索用时 93 毫秒
1.
2.
形式幂级数环R_∞=F[[γ]]={sum from l=0 to a_lγ~l|a_l∈F}与有限链环R_i={a_0+a_1γ+…+a_(i-1)γ~(i-1)|a_i∈F}的码的投影与提升有密切关系.利用形式幂级数环R_∞上码C在有限链环R_i的投影码的自正交性与自对偶性来研究码C的自正交性与自对偶性,得到了两个有意义的结果. 相似文献
3.
本文研究了p-进制环Zp∞={∞∑l=0 alpl|0≤al≤p-1}上线性码的自对偶码的问题.利用p-进制环Zp∞上码C在有限链环Zpα的投影码的自正交性与对偶性,得到了p-进制环上码C的自正交性与对偶性的两个结果. 相似文献
4.
从任意有限环上类型Ⅱ码的概念出发,借助两类有限链环为偶环的特性,研究了其上码为类型Ⅱ码的条件,得到了两个结果. 相似文献
5.
6.
在有限环R=F2+uF2与F2之间定义了一个新的Gray映射,给出了环F2+uF2上线性码C的二元像φ(C)的生成矩阵,证明了环F2+uF2上线性码C及其对偶码的二元像仍是对偶码. 相似文献
7.
8.
假设C是有限域Fq上的[n,κ]线性码,如果码字的每个坐标是其它至多r个坐标的函数,称C是(n,k,r)局部恢复码,这里r是较小的数.在分布式存储系统中,具有多个恢复集的局部恢复码使得数据在系统中更具实际意义,因为它可以避免热数据的频繁访问.引入代数函数域、特别是Hermite函数域去构造局部恢复码,这类局部恢复码具有... 相似文献
9.
引进一个关于Goppa几何码(代数几何码)最小距离界的一个新方法.应用Maharaj的思想(即用显示基来近似表达Riemann-Roch空间)到Goppa几何码的最小距离的界上去.通过厄米特曲线上的代数几何码的一类例子,来证明标准的几何码的下界在某些情形下可以被显著地改进.进一步地,我们给出了这些码的最小距离上界,并说明了我们的下界非常接近这个上界. 相似文献
10.
文章研究了环R=F_4[v]/(v~2+v)上的DNA码.基于环R上长度为n的线性码的代数结构,给出了环R上长度为n的线性码是可逆的DNA码的一个充要条件.同时,给出了环R上长度为n的线性码是可逆补DNA码的一个充要条件. 相似文献
11.
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this work we introduce a new generalization of QT codes that we call multi-twisted (MT) codes and study some of their basic properties. Presenting several methods of constructing codes in this class and obtaining bounds on the minimum distances, we show that there exist codes with good parameters in this class that cannot be obtained as QT or constacyclic codes. This suggests that considering this larger class in computer searches is promising for constructing codes with better parameters than currently best-known linear codes. Working with this new class of codes motivated us to consider a problem about binomials over finite fields and to discover a result that is interesting in its own right. 相似文献
12.
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pair-error correcting performance. Based on repeated-root cyclic codes, we construct two classes of MDS symbol-pair codes for more general generator polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes with the length lp. In addition, we derive all MDS and AMDS symbol-pair codes with length 3p, when the degree of the generator polynomials is no more than 10. The main results are obtained by determining the solutions of certain equations over finite fields. 相似文献
13.
Regarding quasi-cyclic codes as certain polynomial matrices, we show that all reversible quasi-cyclic codes are decomposed into reversible linear codes of shorter lengths corresponding to the coprime divisors of the polynomials with the form of one minus x to the power of m. This decomposition brings us an efficient method to construct reversible quasi-cyclic codes. We also investigate the reversibility and the self-duality of the linear codes corresponding to the coprime divisors of the polynomials. Specializing to the cases where the number of cyclic sections is not more than two, we give necessary and sufficient conditions for the divisors of the polynomials for which the self-dual codes are reversible and the reversible codes of half-length-dimension are self-dual. Our theorems are utilized to search reversible self-dual quasi-cyclic codes with two cyclic sections over binary and quaternary fields of lengths up to seventy and thirty-six, respectively, together with the maximums of their minimum weights. 相似文献
14.
15.
16.
Quantum maximum distance separable (MDS) codes form a significant class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed–Solomon codes, we construct two new classes of -ary quantum MDS codes, which have minimum distance greater than . Most of these quantum MDS codes are new in the sense that their parameters are not covered by the codes available in the literature. 相似文献
17.
The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations. 相似文献
18.
New families of unit memory as well as multi-memory nonbinary convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator matrices, consequently, they are noncatastrophic. Additionally, the new code parameters are better than the ones available in the literature. 相似文献
19.
One of the most important problems of coding theory is to constructcodes with best possible minimum distances. In this paper, we generalize the method introduced by [8] and obtain new codes which improve the best known minimum distance bounds of some linear codes. We have found a new linear ternary code and 8 new linear codes over
with improved minimumdistances. First we introduce a generalized version of Gray map,then we give definition of quasi cyclic codes and introduce nearlyquasi cyclic codes. Next, we give the parameters of new codeswith their generator matrices. Finally, we have included twotables which give Hamming weight enumerators of these new codes. 相似文献