The CRC-CCITT cyclic redundancy check code in international standard is studied in this paper. The polarities check ability, minimum code distance and capacity of correct single bit error of CRC-CCITT are proved by using galois field polynomial theory. 以国际标准CRC-CCITT循环冗余校验码为研究对象,利用近世代数多项式理论证明其奇偶校验性质、最小码距和纠正单比特错误能力。
Finding pseudo noise code with recurrence method and primitive polynomial 用递推法查找伪随机码和本原多项式
Any column of the matrix can be permuted randomly, and the permutation between columns should satisfy the form which is the automorphism group of the binary cyclic Turbo code generated by the feedback polynomial. 该矩阵的任意一列可采用随机交织方式,而列间交织方式必须是按由反馈多项式生成的循环码字集的自同构群构成。
With the give program, one can caculate the system code's CRC check bits for any given system code generator polynomial g ( x) and message code bits at ease. 利用给出的程序,可方便地计算出任意给定的码生成多项式及信息码元下对应的系统码的CRC校验位。
A classical cyclic code over the field GF ( 4) is self-orthogonal with respect to the Hermitian inner product iff the generator polynomial of its dual code is a factor of its generator polynomial. 对于GF(4)上的经典循环码,它是厄米内积自正交的,当且仅当它的对偶码的生成多项式是其生成多项式的因子。
The decoding algorithm is the kernel technique of RS code, and the step-by-step algorithm doesn ′ t need to search the error location polynomial, so it saves the decoding time compared with the traditional ones. 其译码算法是实现RS码的核心,Step-by-step算法与传统的译码算法相比,不用计算错误位置多项式,可以大大地节省译码时间。
NTL is a GNU library and the source code is open for us. It can operate large integer and univariate polynomials, unlucky, it only has the univariate polynomial factorization, no multivariate polynomial factorization. NTL库是开放源代码的自由软件库,它提供了大整数的运算,一元多项式的运算等,遗憾的是,它只提供了一元多项式因式分解,没有提供多元多项式因式分解。