共查询到20条相似文献,搜索用时 218 毫秒
1.
该文定义了环R=F2+uF2+u2F2+u3F2到F24的一个新的Gray映射,其中u4 =0.证明了R上长为n的(1+u+u2 +u3)-循环码的Gray象是F2上长为4n的距离不变的线性循环码.进一步确定了R上奇长度的该常循环码的Gray象的生成多项式,并得到了一些最优的二元线性循环码. 相似文献
2.
在有限环F2+uF2+…+u^k F2与F2之间定义一个新的Gray映射,证明了该映射是距离保持映射。考察了F2+uF2+…+u^k F2环上循环码,得到了F2+uF2+…+u^k F2环上循环码的生成多项式。最后,证明了F2+uF2+…+u^k F2环上循环码在新定义的Gray映射下的像是F2上的准循环码。 相似文献
3.
研究码字的距离分布是编码理论的一个重要研究方向。该文定义了环R=F2+uF2++uk-1F2上的Homogeneous重量,研究了环R上长为2s的(1+u)-常循环码的Hamming距离和Homogeneous距离。使用了有限环和域的理论,给出了环R上长为2s的(1+u)-常循环码和循环自对偶码的结构和码字个数。并利用该常循环码的结构,确定了环R上长为2s的(1+u)-常循环码的Hamming距离和Homogeneous距离分布。 相似文献
4.
5.
6.
7.
研究码字的距离分布是编码理论的一个重要研究方向。该文定义了环R=F2+uF2+…+uk-1F2上的Homogeneous重量,研究了环R上长为2S的(1+u)-常循环码的Hamming距离和Homogeneous距离。使用了有限环和域的理论,给出了环R上长为2S的(1+u)-常循环码和循环自对偶码的结构和码字个数。并利用该常循环码的结构,确定了环R上长为2S的(1+u)-常循环码的Hamming距离和Homogeneous距离分布。 相似文献
8.
9.
10.
11.
12.
San Ling Sole P. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2001,47(7):2751-2760
A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese remainder theorem (CRT), or of the discrete Fourier transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the (u+υ|u-υ) and Vandermonde constructions. All binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced. Other results made possible by the ring decomposition are a characterization of self-dual quasi-cyclic codes, and a trace representation that generalizes that of cyclic codes 相似文献
13.
14.
Lally K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2006,52(5):2101-2110
A new module structure for convolutional codes is introduced and used to establish further links with quasi-cyclic and cyclic codes. The set of finite weight codewords of an (n,k) convolutional code over Fq is shown to be isomorphic to an Fq[x]-submodule of Fq n[x], where Fq n[x] is the ring of polynomials in indeterminate x over Fq n, an extension field of Fq. Such a module can then be associated with a quasi-cyclic code of index n and block length nL viewed as an Fq[x]-submodule of Fq n[x]/langxL-1rang, for any positive integer L. Using this new module approach algebraic lower bounds on the free distance of a convolutional code are derived which can be read directly from the choice of polynomial generators. Links between convolutional codes and cyclic codes over the field extension Fq n are also developed and Bose-Chaudhuri-Hocquenghem (BCH)-type results are easily established in this setting. Techniques to find the optimal choice of the parameter L are outlined 相似文献
15.
Lachaud G. Wolfmann J. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1990,36(3):686-692
Starting from results on elliptic curves and Kloosterman sums over the finite field GE(2t), the authors determine the weights of the orthogonals of some binary linear codes; the Melas code of length, the irreducible cyclic binary code of length 2t+1, and the extended binary Goppa codes defined by polynomials of degree two 相似文献
16.
Aydin N. Ray-Chaudhuri D.K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2002,48(7):2065-2069
Previously, (linear) codes over Z 4 and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z 4-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z 4 produces a new binary code, a (92, 224, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials 相似文献
17.
Cyclic codes and self-dual codes over F2+uF2 总被引:1,自引:0,他引:1
Bonnecaze A. Udaya P. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1999,45(4):1250-1255
We introduce linear cyclic codes over the ring F2+uF 2={0,1,u,u¯=u+1}, where u2=0 and study them by analogy with the Z4 case. We give the structure of these codes on this new alphabet. Self-dual codes of odd length exist as in the case of Z4-codes. Unlike the Z4 case, here free codes are not interesting. Some nonfree codes give rise to optimal binary linear codes and extremal self-dual codes through a linear Gray map 相似文献
18.
《IEEE transactions on information theory / Professional Technical Group on Information Theory》1978,24(5):628-630
An integer linear programming problem and an additional divisibility condition are described such that they have a common solution if and only if there is a quasi-cyclic code with rate1/m . A table of binary quasi-cyclic codes with dimensions seven and eight and rate1/m for smallm is included. In particular, there are binary linear codes with (length, dimension, minimum distance)=(35, 7,16), (42, 7,19), (80, 8, 37), (96, 8, 46) , and(112,8,54) . 相似文献
19.
A 2-adic approach to the analysis of cyclic codes 总被引:2,自引:0,他引:2
Calderbank A.R. Wen-Ching Winnie Li Poonen B. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1997,43(3):977-986
This paper describes how 2-adic numbers can be used to analyze the structure of binary cyclic codes and of cyclic codes defined over Z 2(a), a⩾2, the ring of integers modulo 2a. It provides a 2-adic proof of a theorem of McEliece that characterizes the possible Hamming weights that can appear in a binary cyclic code. A generalization of this theorem is derived that applies to cyclic codes over Z 2(a) that are obtained from binary cyclic codes by a sequence of Hensel lifts. This generalization characterizes the number of times a residue modulo 2a appears as a component of an arbitrary codeword in the cyclic code. The limit of the sequence of Hensel lifts is a universal code defined over the 2-adic integers. This code was first introduced by Calderbank and Sloane (1995), and is the main subject of this paper. Binary cyclic codes and cyclic codes over Z 2(a) are obtained from these universal codes by reduction modulo some power of 2. A special case of particular interest is cyclic codes over Z 4 that are obtained from binary cyclic codes by means of a single Hensel lift. The binary images of such codes under the Gray isometry include the Kerdock, Preparata, and Delsart-Goethals codes. These are nonlinear binary codes that contain more codewords than any linear code presently known. Fundamental understanding of the composition of codewords in cyclic codes over Z 4 is central to the search for more families of optimal codes. This paper also constructs even unimodular lattices from the Hensel lift of extended binary cyclic codes that are self-dual with all Hamming weights divisible by 4. The Leech lattice arises in this way as do extremal lattices in dimensions 32 through 48 相似文献
20.
Kerdock码和Preparata码是两类著名的二元非线性码,它们比相同条件下的线性码含有更多的码字.Hammons等人在1994年发表的文献中证明了这两类码可视为环Z4上循环码在Gray映射下的像,从而使得这两类码的编码和译码变得非常简单.环F2+uF2是介于环Z4与域F4之间的一种四元素环,因此分享了环Z4与域F4的一些好的性质,此环上的编码理论研究成为一个新的热点.本文首次将Kerdock码和Preparata码的概念引入到环Fp+uFp上,证明了它们是一对对偶码;并给出Kerdock码的迹表示;当p=2时,建立了环F2+uF2上这两类码与域F2上的Reed-Muller码之间的联系;并证明了二元一阶Reed-Muller码是环F2+uF2上Kerdock码的线性子码的Gray像. 相似文献