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As to cyclic codes over finite chain rings, we study their stucture and develop the Fourier Transform method to finite chain rings. The permutation groups of cyclic codes and their extended codes are investigated using their Mattson-Solomn polynomials.

对于有限链环上的循环码,我们研究了它们的结构,并把傅立叶变换的方法推广到有限链环,用循环码的Mattson-Solomn多项式对循环码及其扩展码的置换群进行了研究。

The permutation groups of cyclic codes and their extended codes are investigated using their Mattson-Solomn polynomials. SDq codes over finite fields are byte-organized and they can correct any single error and dete

有限域上的SD_q码是一类按字节组织的,能纠正发生的所有单个错误,同时能检测发生在同一字节内的两个相邻错误的纠错码;我们对有限域F_q上SD_q码的线对界在q>3,b>2时给出了一个改进界。

Recently, many coding experts have studied much of the Z_4-cyclic code(which is not necessarily linear) and its Gray map, and obtained a set of equivalent conditions in which a family of cyclic codes are linear, and the condition that this family codes are self-dual cyclic, and in this condition Nechaev-Gray image of the cyclic codes are self-dual cyclic.

近年来,已有编码学家对Z 4-循环码和Z 4上的映射作了深入研究,得到一类循环码是线性码的一系列等价条件,以及这类线性码是自对偶线性循环码的条件,在此条件下它的Nechaev-Gray像也是自对偶线性循环码。

The 1-generator quasi-cyclic codes and their duals are the most frequently encountered QC codes in the literature. Séguin discusses the construction and the enumeration of 1-generator QC codes in the special case where the prime factorization of x~m — 1 is the same in IF_qn as in IF_q.

单生成元的拟循环码及其对偶码是拟循环码中研究最多的一种。Séguin在要求x~m-1在F_q及F_中具有相同的分解的条件下,讨论了单生成元的拟循环码的结构及计数。

In this dissertation, it is showed that, in the split linear case, and are precisely the expurgated quadratic residue codes and , respectively, from which one can study the quantum quadratic residue codes via the quadratic residue codes.

本文证明了分裂型线性量子二次剩余码的两个相伴码和恰好就是经典删余二次剩余码和,由此我们可以通过经典二次剩余码理论来研究量子二次剩余码。

On the basis of standard codes,corresponding revisal codes are also adopted to express the deviation from standard codes.

在此基础上,进一步确定曲线的修正编码,以表示曲线与标准编码的差异程度。

The generalized Reed-Solomon codes over the finite field F_q aremaximum-distance separable codes. This class of codes has optimal parameters.

利用有限域F_q中元来构造广义Reed-Solomon码,它是极大距离可分码,码的参数达到最优,但码的长度至多为q。

LDPC has more excellent performance than Turbo codes、convolve codes or others in many aspects.So LDPC codes combining with OFDM would have academic and practical significance.

由于LDPC码在很多方面具有比Turbo码、卷积码等更优的性能,将LDPC码与OFDM技术结合应用成为了论文研究工作的核心,这将会有十分重要的理论和实践意义。

The Turbo-codes encoder is comprised of Recursive Systematic Convolutional Codes, which is connected by an interweaver. And the decoding algorithm of Turbo-codes, such as MAP, Max-log-MAP and SOVA, are all based on the soft input and soft output module.

传统的Turbo码山两个经交织器连接的分量码编码器级联而成,且Turbo码的译码采用了软输入软输出的算法思想和迭代译码的方法,使子译码器之间可以相互传递软信息,保证编码信息的充分利用。

The 43 table of genetic codes is in fact that 64 segments of spacial room in real DNA molecule versus a real molecule of amino acids in protein , which is an obvious logical error .4.Each relevant experiment proved the table of genetic codes has its own permutable pattern from chemical reactants to products , instead of the descriptions in the table of genetic codes .

密码表应用体系中,从DNA分子到m RNA分子到t RNA,再到核糖体到肽链,没有一步使用了排列数计算方法,从而造成DNA分子信息传递时步步失真,最后变成了肽链具体位置上的氨基酸分子,这里的每一步信息传递都是对密码表的错误运用。

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