Qr code is a kind of 2d matrix barcode . it has high density , great capacity that will influent coding of 2d - barcode . a rs code is cyclic symbol error - correcting code , which can correct lost or missing data for damaged symbols Qrcode是一种矩阵二维码，具有信息密度大、容量高的优点，因此，译码时受噪声的干扰大，采用纠错能力比较强的非二进制bch码中的一类? rs码进行编码，可以有效地抗除干扰进行纠错。
Some results on the undetected error probability of linear codes for pure error - detection are , at present , generalized for both error detection and correction . an analytic formula is obtained to calculate the undetected error probability of linear block codes for simultaneous error detection and correction 在只检错时，证明了纠正两个错误扩展bch码是最佳检错码； m大于4的非线性等重码( 2m ， 2 ， m )不是最佳码。
The flex decoder designed in this paper includes the physical layer block , the date link layer block , the bch decoder and the spi interface circuit . the configuration of mcu is adopted in the design of the bch decoder , which make the bch decoder has simple structure and high decoding speed 该设计采用自顶向下的设计方法，对flex解码系统进行功能层次上的划分，系统主要包括：物理层处理模块，数据链路层处理模块，解码及纠错模块，以及数据接收和发送模块。
Researches the basis watermark managing works particularly and systemly . there are many works to do on watermak technology except watermark embedding and extraction arithmetics such as the watermark choosing , encoding , modulating , demodulating and the watermark capacity . these prior and ultimate works ensure that the arithmetic is brought into effect . just understanding these , this paper analyses and researches the basic watermark theoretics in many pages . it brings forward chaos modulation on watermark modulating , brings forward chaos permuting on image permuting , introduces bch encoding on letter watermark processing and discusses the approximate estimate of the watermark capacity in dct domain and dwt domain by applying the current communication theoretics . there works not only extend ways for the later work but also are significative on watermark research 全面系统地研究了水印信号的处理技术数字水印技术除了水印嵌入和提取的算法外，还有许多工作需要做，如水印的选码、编码、调制、解调、能量的确定等等，这些预处理和后处理工作是算法有效实施的必要保证，正是基于这样的认识，本文利用较大的篇幅对水印的基本理论知识进行了详细的分析和研究，在水印的调制方面，提出了混沌调制法；在图像水印的置乱方面，提出了混沌置乱法；在文字水印的处理上，引入了bch编码；在水印容量分析方面，结合现代通信理论，对图像在dct域和小波域内的水印容量估算进行了详细的探讨，这些工作不仅为本文后期工作铺平了道路，而且对数字水印的研究具有重要的意义。
Official languages authentic chinese text merchant shipping prevention of oil pollution regulation , merchant shipping control of pollution by noxious liquid substances in bulk regulations , merchant shipping reporting of pollution incidents regulations , merchant shipping bch code regulations , merchant shipping ibc code regulations and merchant shipping prevention of oil pollution regulations exemption notice order 21 .法定语文中文真确本商船防止油类污染规例商船控制散装有毒液体物质污染规例商船报告污染事故规例商船散化
Is the eth residue of p . since the number of quadratic residue mod p is , we can guess the number of eth residue mod p is 2 ^ , and then prove this property . on the basis of eth residue , we construct a type of eth residue code of length p which is an odd prime , and extend some properties of quadratic residue codes . alsi ) we construct a cubic residue code over f % of length 31 and a 4th residue code over fs of length 13 . according to the properties of the bounds of bch codes , we determine the minimal distance of [ 31 , 21 ] code is 5 , which means this code ; can correct two errors 由模p的二次剩余个数为个，可猜测模p的e次剩余的个数为个，本文给出了该性质的证明。在e次剩余的基础上，本文构造了一类字长p为奇素数的e次剩余码，讨论了它的性质，从而推广了二次剩余码的一些结果。利用所导出的理论结果，我们构造了长为31的二元三次剩余码和长为13的三元四次剩余码，利用bch码上下界的性质，进一步确定了31 ， 21码的极小距离为5 ，它可以纠正两个错误。
More and more people begin to attach importance to its potence gradually . according to the basic principle of vbi , this paper acquires related experience from the advanced technique for delivering of control signals during the period of vbi . it introduces a scheme using a single coaxial - cable to transmit video signals and control signals simultaneously , in which the key technique is the transmission of control signals in the vertical blanking interval of video signals 本文根据场消隐期传输技术的基本原理，通过借鉴国内外场消隐期传输信号的先进技术和相关经验，提出一种新型的综合数据传输业务的应用电视，阐述了其图像信号和控制信号共缆传输的总体设计方案，并结合bch纠错编解码技术和systemview动态仿真软件，实现和验证了控制信号在场消隐期间的稳定可靠传输。
In order to keep the signal transmission unfailing , bch error - correcting code is applied in the system . this kind of system does n ' t affect the application television broadcasting normally and does n ' t increase video signal bandwidth additionally . it optimizes the transmission circuit for control signals and solves the problem of time - delaying , thereby it promotes the transmission more efficiently and economically 这种新型的应用电视在不影响电视正常播放和不增加电视传输带宽的前提下，将控制信号搭载在视频信号通道上运行，优化了控制信号传输线路，解决了时延问题，达到了利用电视信号逆程资源的目的，真正意义上实现了单缆传输监控系统，促进了监控系统的高效化和经济化。
At last , by using the factorization properties of cyclotomic polynmials on finite fields and the construction characteristic of cyclic codes , we present the relation of the period distribution of cyclic codes and the period distribution of their dual codes , establish the explicit formula for the number of the codewords without inner - period of the cyclic codes and their dual codes , find the method for computing the dimension and the period distribution of narrow - sense primitive bch codes , and study the inverse question of period distribution of cyclic codes 最后，利用有限域上分圆多项式的分解特性和循环码的构造特点，揭示了循环码的周期分布与其对偶码周期分布之间的内在联系，确定了一般循环码及其对偶码内无内周期码字的精确计数公式，决定了狭义本原bch码的维数与周期分布，讨论了循环码周期分布的反问题。
The concept of good codes and proper codes for both error detection and correction is presented . it is shown that the binary perfect codes and the primitive double - error - correcting bch codes and their extended codes are proper for both error detection and correction . the primitive triple - error - correcting bch codes with length 2 " " - 1 and their extended codes are proper for odd m > 5 , not for even m > 6 本文的主要工作是把目前关于只检错时线性码不可检错误概率的研究推广到同时纠错和检错的情况，获得了同时纠检错时线性码不可检错误概率的解析表达式，提出了纠检错好码和最佳纠检错码的概念，并证明了二进制完备码及其扩展码是最佳纠检错码；纠正两个错误二进制本原bch码及其扩展码是最佳纠检错码；码长n = 2 ~ m - 1 、纠正三个错误本原bch码，当m为大于等于5的奇数时是最佳纠检错码；当m为大于等于6的偶数时，不是最佳码。
