共查询到19条相似文献,搜索用时 79 毫秒
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为了讨论二元Reed-Muller码的 Z4 线性, 文献中先后介绍了两类 Z4 线性码, 分别记为ZRM}(r, m)与QRM}(r, m), 它们在Gray映射下的二元像记为ZRM}(r, m)与 QRM}(r, m) . 该文系统地讨论了这两类 Z4 线性码. 计算了ZRM}(r, m)与QRM}(r, m)的类型, 证明当3≤r≤m-1时, ZRM}(r, m)是二元线性码, 而QRM}(r, m)是非线性的; 并且, 由QRM}(r, m)张成的二元线性码恰是ZRM}(r, m). 最后, 对于非线性码QRM}(r, m), 讨论了它的秩与核. 相似文献
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本文研究了环F2m+uF2m+u2 Fm+u3F2m上线性码.利用环是Frobenius环,证明了环上线性码C及其自对偶码的Gray像为F2m上的线性码和自对偶码.同时,给出了上循环码C的Gray像ψ(C)为F2m上的拟循环码. 相似文献
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我们记Tk为Galois环GR(2^k,m)到Z2^k的迹映射,ξ是GR(2^k,m)中的本原元,ξ2^m-1=1,ιk,m={0,1,ξ,…,ξ2^m-2},来讨论一类Z2^k-线性码{Tk(a0x 2^k-2a1x^3 2^k-1,a2x^5) b|a0∈GR(2^k,m),a1∈ιk,m 2ιk,m,a2∈ιk,m,b∈Z2^k}x∈ιk的广义Gray映射下的象所构成的二元码,这类二元码也具有很好的参数性质,优于一些已知的二元码,例如广义的Kerdock码或广义的Delsarte-Goethals码。 相似文献
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三维七元线性码的重量谱与改进的遗传算法 总被引:1,自引:0,他引:1
[n,3,7]线性码的重量谱与其差序列是一一对应的。本文改进了[1]结构4的条件(iv),从而得到了不满足链条件的[n,3;7]线性码的差序列的充要条件,并应用改进的遗传算法搜索满足链条件的[n,3;7]线性码的差序列,取得了较好的结果。 相似文献
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本文研究了卡氏积码的r-广义Hamming重量计算公式和广义Singleton界,利用r-卡氏积码的子码仍为卡氏积码,证明了r-MDR码或Pr-MDR码的卡氏积码仍为r-MDR码或Pr-MDR码.同时也给出了这一个结果的部分逆命题. 相似文献
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利用不同的序列作为波长跳频序列和时间扩频序列可以构造出不同的二维光正交码在众多文献中已有所报道.在经过正交拉丁方(OLS)与跳频序列的相关性研究之后.做了以下主要工作:首先,将正交拉丁方(OLS)序列作为波长跳频序列,结合一维时间扩频序列(OOC),构造了一种OLS/OOC二维光正交码.然后,本文对构造的OLS/OOC进行了多种性能仿真和分析.相对于PC/OOC、OCFHC/OOC等二维光正交码而言,OLS/OOC的波长数并不局限于素数,更能充分利用MWOCDMA系统中的有效波长数.仿真和分析表明:码字具有很好的相关性能,码字容量直逼理论极限,为一种渐近最优二维光正交码. 相似文献
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In Duursma and Park (2010) [7], the authors formulate new coset bounds for algebraic geometric codes. The bounds give improved lower bounds for the minimum distance of algebraic geometric codes as well as improved thresholds for algebraic geometric linear secret sharing schemes. The bounds depend on the delta set of a coset and on the choice of a sequence of divisors inside the delta set. In this paper we give general properties of delta sets and we analyze sequences of divisors supported in two points on Hermitian and Suzuki curves. 相似文献
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Khmaies Ouahada Theo G. Swart Hendrik C. Ferreira Ling Cheng 《Designs, Codes and Cryptography》2008,48(2):141-154
We investigate binary sequences which can be obtained by concatenating the columns of (0,1)-matrices derived from permutation
sequences. We then prove that these binary sequences are subsets of a surprisingly diverse ensemble of codes, namely the Levenshtein
codes, capable of correcting insertion/deletion errors; spectral null codes, with spectral nulls at certain frequencies; as
well as being subsets of run-length limited codes, Nyquist null codes and constant weight codes.
This paper was presented in part at the IEEE Information Theory Workshop, Chengdu, China, October, 2006. 相似文献
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Very odd sequences were introduced in 1973 by Pelikán who conjectured that there were none of length 5. This conjecture was disproved first by MacWilliams and Odlyzko [17] in 1977 and then by two different sets of authors in 1992 [1], 1995 [9]. We give connections with duadic codes, cyclic difference sets, levels (Stufen) of cyclotomic fields, and derive some new asymptotic results on the length of very odd sequences and the number of such sequences of a given length. 相似文献
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Pierre-Louis Cayrel Christophe Chabot Abdelkader Necer 《Finite Fields and Their Applications》2010,16(2):100-115
Quasi-cyclic codes over a finite field are viewed as cyclic codes over a noncommutative ring of matrices over a finite field. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction of some quasi-cyclic codes and self-dual codes. 相似文献
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Terje O. Espelid 《BIT Numerical Mathematics》2003,43(2):319-337
In this paper we test two recently published Matlab codes, adaptsim and adaptlob, using both a Lyness–Kaganove test and a battery type of test. Furthermore we modify these two codes using sequences of null rules in the error estimator with the intention to increase the reliability for both codes. In addition two new Matlab codes applying a locally and a globally adaptive strategy respectively are developed. These two new codes turn out to have very good properties both with respect to reliability and efficiency. Both algorithms are using sequences of null rules in their local error estimators. These error estimators allow us both to test if we are in the region of asymptotic behavior and thus increase reliability and to take advantage of the degree of precision of the basic quadrature rule. The new codes compare favorably to the two recently published adaptive codes both when we use a Lyness–Kaganove testing technique and by using a battery test. 相似文献
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We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in PG(4,q) to find information about the LDPC codes defined by Q (4,q), and . For , and , we are able to describe small weight codewords geometrically. For , q odd, and for , we improve the best known lower bounds on the minimum distance, again only using geometric arguments. Similar results are also presented for the LDPC codes LU(3,q) given in [Kim, (2004) IEEE Trans. Inform. Theory, Vol. 50: 2378–2388] 相似文献
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Negacyclic codes of length 2s over the Galois ring GR(2a,m) are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals <(x + 1)i>,0 ≤ i ≤ 2sa,of the chain ring GR(2a,m)[x]/.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m (i.e.,a =1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2s over F2m. 相似文献
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Previous results have shown that the class of quasi-cyclic (QC) codes contains many good codes. In this paper, new rate (m - 1)/pm QC codes over GF(3) and GF(4) are presented. These codes have been constructed using integer linear programming and a heuristic combinatorial optimization algorithm based on a greedy local search. Most of these codes attain the maximum possible minimum distance for any linear code with the same parameters, i.e., they are optimal, and 58 improve the maximum known distances. The generator polynomials for these 58 codes are tabulated, and the minimum distances of rate (m - 1)/pm QC codes are given. 相似文献
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Maximum rank-distance (MRD) codes are extremal codes in the space of \(m\times n\) matrices over a finite field, equipped with the rank metric. Up to generalizations, the classical examples of such codes were constructed in the 1970s and are today known as Gabidulin codes. Motivated by several recent approaches to construct MRD codes that are inequivalent to Gabidulin codes, we study the equivalence issue for Gabidulin codes themselves. This shows in particular that the family of Gabidulin codes already contains a huge subset of MRD codes that are pairwise inequivalent, provided that \(2\leqslant m\leqslant n-2\). 相似文献