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本文研究了Goppa码、BCH码的广义Hamming重量,给出了Goppa码的广义Hamming重量的一个下界以及求该下界的一个算法;对于本原、狭义BCH码,给出了后面一些广义Hamming重量的确切值。 相似文献
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关于BCH码的广义Hamming重量 总被引:3,自引:0,他引:3
文中研究了本原狭义BCH码的广义Hamming首先给出一般的BCH码的广义Hamming重量下界,然后对于最后了一些广义Hamming重量,我们给出了确切值。 相似文献
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关于BCH码的广义Hamming重量上,下限 总被引:2,自引:0,他引:2
一个线性码的第r广义Hamming重量是它任意r维子码的最小支集大小。本文给出了一般(本原、狭义)BCH码的广义Hamming重量下限和一类BCH码的广义Hamming重量上限 相似文献
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广义Hamming重量和等重码 总被引:8,自引:0,他引:8
本文将线性码的广义Hamming重量的概念推广到线性码上去,并导出了一种广义Elias界,对于线性等重码,本文给出了其完整的重量谱系。 相似文献
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关于Goppa码、BCH码的广义Hamming重量 总被引:1,自引:0,他引:1
本文研究了Goppa码、BCH码的广义Hamming重量,给出了Goppa码的广义Hamming重量的一个下界以及求该下界的一个算法;对于本原、狭义BCH码,给出了后面一些广义Hamming重量的确切值。 相似文献
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等距码的对偶距离分布及其性质 总被引:5,自引:2,他引:3
本文主要讨论了等距码的对偶距离分布及其性质,然后利用这些性质将[1]中的某些结果推广到q元等距码情形,并得到了其对偶距离分布的递推关系式,最后,本文给出了q元等距码的码字数目的一个上界。 相似文献
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环E+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。该文给出了环E+uF2的Galois扩张的相关理论,指出此Galois扩环的自同构群不同于Z4环上的Galois扩环的自同构群;定义了Galois扩环上的迹码的概念及子环子码的概念,证明了此Galois扩环上的一个码的对偶码的迹码是该环的子环子码的对偶码。 相似文献
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Feng G.L. Tzeng K.K. Wei V.K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(3):1125-1130
The generalized Hamming weights of a linear code are fundamental code parameters related to the minimal overlap structures of the subcodes. They were introduced by V.K. Wei (1991) and shown to characterize the performance of the linear code in certain cryptographical applications. Results are presented on the generalized Hamming weights of several classes of binary cyclic codes, including primitive double-error-correcting and triple-error-correcting BCH codes, certain reversible cyclic codes, and some extended binary Goppa codes. In particular, the second generalized Hamming weight of primitive double-error-correcting BCH codes is determined and upper and lower bounds are obtained for the generalized Hamming weights for the codes studied. These bounds are compared to results from other methods 相似文献
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Changshik Shim Habong Chung 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1995,41(3):805-808
The generalized Hamming weight of a linear code is a new notion of higher dimensional Hamming weights. Let C be an [n,k] linear code and D be a subcode. The support of D is the cardinality of the set of not-always-zero bit positions of D. The rth generalized Hamming weight of C, denoted by dr(C), is defined as the minimum support of an r-dimensional subcode of C. It was shown by Wei (1991) that the generalized Hamming weight hierarchy of a linear code completely characterizes the performance of the code on the type II wire-tap channel defined by Ozarow and Wyner (1984). In the present paper the second generalized Hamming weight of the dual code of a double-error-correcting BCH code is derived and the authors prove that except for m=4, the second generalized Hamming weight of [2m-1, 2m]-dual BCH codes achieves the Griesmer bound 相似文献
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Levy-dit-Vehel F. Litsyn S. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1997,43(6):1811-1819
We discuss parameters of Goppa (1970) codes, such as minimum distance, covering radius, distance distribution, and generalized Hamming weights. By a variation on the exponential sums method and combinatorial arguments, we sharpen known bounds on these parameters 相似文献
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Generalized Hamming weights of q-ary Reed-Muller codes 总被引:3,自引:0,他引:3
Heijnen P. Pellikaan R. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1998,44(1):181-196
The order bound on generalized Hamming weights is introduced in a general setting of codes on varieties which comprises both the one point geometric Goppa codes as well as the q-ary Reed-Muller codes. For the latter codes it is shown that this bound is sharp and that they satisfy the double chain condition 相似文献
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V. B. Afanassiev A. A. Davydov D. K. Zigangirov 《Journal of Communications Technology and Electronics》2017,62(6):669-685
The conditional probability (fraction) of the successful decoding of erasure patterns of high (greater than the code distance) weights is investigated for linear codes with the partially known or unknown weight spectra of code words. The estimated conditional probabilities and the methods used to calculate them refer to arbitrary binary linear codes and binary Hamming, Panchenko, and Bose–Chaudhuri–Hocquenghem (BCH) codes, including their extended and shortened forms. Error detection probabilities are estimated under erasure-correction conditions. The product-code decoding algorithms involving the correction of high weight erasures by means of component Hamming, Panchenko, and BCH codes are proposed, and the upper estimate of decoding failure probability is presented. 相似文献
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Moreno C.J. Moreno O. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1992,38(4):1222-1229
For pt.I, see Proc. AMS, vol.III, p.523-31 (1991). The minimum distance of a Goppa code is found when the length of code satisfies a certain inequality on the degree of the Goppa polynomial. In order to do this, conditions are improved on a theorem of E. Bombieri (1966). This improvement is used also to generalize a previous result on the minimum distance of the dual of a Goppa code. This approach is generalized and results are obtained about the parameters of a class of subfield subcodes of geometric Goppa codes; in other words, the covering radii are estimated, and further, the number of information symbols whenever the minimum distance is small in relation to the length of the code is found. Finally, a bound on the minimum distance of the dual code is discussed 相似文献
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Justesen J. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2004,50(2):350-353
We derive upper bounds on the weights of error patterns that can be corrected by a convolutional code with given parameters, or equivalently we give bounds on the code rate for a given set of error patterns. The bounds parallel the Hamming bound for block codes by relating the number of error patterns to the number of distinct syndromes. 相似文献