共查询到16条相似文献,搜索用时 109 毫秒
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纠错码是提高信息传输效率与可靠性的重要手段.构造性能良好的线性码类是纠错码研究中的一个基本问题.本文主要讨论了有限非链环Fq[v]/(vm-v)上自对偶常循环码的代数结构,包括Euclidean自对偶常循环码、Hermitian自对偶常循环码以及Hermitian自对偶常循环码的极大距离可分(MDS)码.本文给出了环Fq[v]/(vm-v)上常循环码是Euclidean自对偶码的充分条件,以及是Hermitian自对偶码的充要条件,并利用Gray映射构造了有限域Fq上一些参数较好的自对偶码.特别地,本文得到了有限域F192上一个新的参数为[16,8,6]的Hermitian自对偶码. 相似文献
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首先给出了环R=Fp+vFp+v2Fp上线性码及其对偶码的结构及其Gray象的性质.定义了环R上线性码的各种重量计数器并讨论了它们之间的关系,特别的,确定了该环上线性码与其对偶码之间关于完全重量计数器的MacWilliams恒等式,利用该恒等式,进一步建立了该环上线性码与其对偶码之间的一种对称形式的MacWilliams恒等式.最后,利用该对称形式的MacWilliams恒等式得到了该环上的Hamming重量计数器和Lee重量计数器的MacWilliams恒等式,利用不同的方法推广了文献[7]中的结果. 相似文献
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基于环Fp+vFp(v2=v)上线性码的一种直和分解,利用环Fp+vFp上的线性码的Torsion码,把环Fp+vFp上的线性码的极小支座谱的确定归结于有限域上的情形;进一步探讨了环Fp+vFp上的线性码的校验矩阵,利用该校验矩阵确定了环Fp+vFp上的线性码的对偶码的极小支座谱;最后利用环上的线性码的极小支座谱,探讨了环Fp+vFp上线性码的最小Hamming距离,并且给出了一个环Fp+vFp上最小Hamming距离为d的线性码的构造方法,这里p是任一个素数,d是一个正整数. 相似文献
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Shadow codes and weight enumerators 总被引:1,自引:0,他引:1
Dougherty S.T. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1995,41(3):762-768
The technique of using shadow codes to build larger self-dual codes is extended to codes over arbitrary fields. It is shown how to build the codes and how to determine the new weight enumerator as well. For codes over fields equipped with a square root of -1 and not of characteristic 2, a self-dual code of length n+2 can be built from a self-dual code of length n; for codes over a field without a square root of -1 and not of characteristic 2 a self-dual code of length n+4 is built from a self-dual code of length n; and for codes over fields of characteristic 2 the length of the new self-dual code depends on the presence of the all-one vector in the subcode chosen. In certain cases using the subcode of vectors orthogonal to the all-one vector, the new weight enumerator can be calculated directly from the original weight enumerator. Specific examples of the technique are illustrated for codes over F3, F4, and F5 相似文献
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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
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Sundeep B Thangaraj A. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2007,53(7):2480-2489
A code over GF can be imaged or expanded into a code over GF using a basis for the extension field over the base field. The properties of such an image depend on the original code and the basis chosen for imaging. Problems relating the properties of a code and its image with respect to a basis have been of great interest in the field of coding theory. In this work, a generalized version of the problem of self-orthogonality of the q-ary image of a qm-ary code has been considered. Given an inner product (more generally, a bi-additive form), necessary and sufficient conditions have been derived for a code over a field extension and an expansion basis so that an image of that code is self-orthogonal. The conditions require that the original code be self-orthogonal with respect to several related bi-additive forms whenever certain power sums of the dual basis elements do not vanish. Numerous interesting corollaries have been derived by specializing the general conditions. An interesting result for the canonical or regular inner product in fields of characteristic two is that only self-orthogonal codes result in self-orthogonal images. Another result is that image of a code is self-orthogonal for all bases if and only if trace of the code is self-orthogonal, except for the case of binary images of 4-ary codes. The conditions are particularly simple to state and apply for cyclic codes. To illustrate a possible application, new quantum error-correcting codes have been constructed with larger minimum distance than previously known. 相似文献