- all of the cyclic codes over the galois ring gr ( 4m ) , and the bases for gr ( 4m ) over z4 are determined , such that with respect to the bases , the 4 - ary image of the cyclic codes are still cyclic 對于伽羅華環(huán)gr ( 4 ~ m )上的一類循環(huán)碼,以及gr ( 4 ~ m )在z _ 4上的一組基,給出了滿足這類循環(huán)碼相對于該組基展開后得到的碼是四元循環(huán)碼的充分必要條件,該條件簡便實用; 5
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 對于有限鏈環(huán)上的循環(huán)碼,我們研究了它們的結(jié)構(gòu),并把傅立葉變換的方法推廣到有限鏈環(huán),用循環(huán)碼的mattson - solomn多項式對循環(huán)碼及其擴展碼的置換群進行了研究。
Based on the group theoretic framework , equivalent forms of quantum error correcting codes are found for encoding three qubits in eight qubits and correcting one error . a class of quantum cyclic codes of encoding one qubit and correcting two or three random quantum errors is obtained via quadratic residue 第四章研究了量子糾錯碼,基于群論框架求出了量子8編3碼的等價碼,用二次剩余方法求出了一類糾兩位和三位錯的量子碼。
The distributed plc system of the floodgate ' s opening measuring presented by the paper has many advantages such as high reliable operation , high measuring precision , having the network communication function , convenient installation and correction , etc . this thesis further studies the key device for the floodgate ' s opening measuring , the rotary encoder , selects the absolute rotary encoder adopting the binary cyclic code , studies the method for transforming the cyclic code to the binary data and according to the transforming formula designs the ladder diagram program 本論文研制的分布式plc閘門開度測量系統(tǒng)具有工作可靠、測量精度高、具有聯(lián)網(wǎng)通信功能、安裝和校正方便等特點。本論文深入研究了閘門開度檢測的關(guān)鍵器件? ?旋轉(zhuǎn)編碼器,選用了采用二進制循環(huán)碼編碼的絕對式旋轉(zhuǎn)編碼器,研究了將二進制循環(huán)碼轉(zhuǎn)換為二進制數(shù)的方法,根據(jù)轉(zhuǎn)換公式設(shè)計了plc的梯形圖轉(zhuǎn)換程序。
In the gsm system , error - control is the key - technology of the wireless - interface . combining the error - control technology with the software and hardware , in the baseband transmit part of the gsm mobile station test set , i ' ll provide a module which can accomplish the physical layer ' s protocol of the wireless - interface . , and the fec technologies , such as cyclic code , convolutional code and viterbi decode , can be achieved by the baseband module , too 差錯控制技術(shù)是gsm移動通信系統(tǒng)無線接口協(xié)議的核心內(nèi)容,本課題的任務(wù)是將差錯控制技術(shù)的原理與相關(guān)的軟、硬件結(jié)合起來,在gsm移動電話綜合測試儀的數(shù)字基帶模塊中實現(xiàn)gsm無線接口的物理層協(xié)議,完成差錯控制技術(shù)中的循環(huán)碼、卷積碼、交織、 viterbi譯碼等前向糾錯技術(shù)。
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,利用有限域上分圓多項式的分解特性和循環(huán)碼的構(gòu)造特點,揭示了循環(huán)碼的周期分布與其對偶碼周期分布之間的內(nèi)在聯(lián)系,確定了一般循環(huán)碼及其對偶碼內(nèi)無內(nèi)周期碼字的精確計數(shù)公式,決定了狹義本原bch碼的維數(shù)與周期分布,討論了循環(huán)碼周期分布的反問題。
In coding theory, cyclic codes are linear block error-correcting codes that have convenient algebraic structures for efficient error detection and correction.