公开(公告)号：US20020170018A1

公开(公告)日：2002-11-14

申请号：US09842244

申请日：2001-04-24

申请人： International Business Machines Corporation

发明人： Charles Edwin Cox ,  Martin Aureliano Hassner ,  Barry Marshall Trager ,  Shmuel Winograd

IPC分类号： H03M013/00 ,  H04L001/00 ,  G06F011/00

CPC分类号： H03M13/1545 ,  H03M13/1515

摘要： An error correction algebraic decoder uses a key equation solver for calculating the roots of finite field polynomial equations of degree up to six, and lends itself to efficient hardware implementation and low latency direction calculation. The decoder generally uses a two-step process. The first step is the conversion of quintic equations into sextic equations, and the second step is the adoption of an invertible Tschirnhausen transformation to reduce the sextic equations by eliminating the degree 5 term. The application of the Tschirnhausen transformation considerably decreases the complexity of the operations required in the transformation of the polynomial equation into a matrix. The second step defines a specific Gaussian elimination that separates the problem of solving quintic and sextic polynomial equations into a simpler problem of finding roots of a quadratic equation and a quartic equation.

摘要翻译： 纠错代数解码器使用密钥方程求解器来计算六个有限域多项式方程的根，并适用于有效的硬件实现和低延迟方向计算。 解码器通常采用两步法。 第一步是将五次方程转换为性别方程，第二步是采用可逆的Tschirnhausen变换，通过消除5度项来减少性别方程。 Tschirnhausen变换的应用大大降低了将多项式方程转换为矩阵所需的操作的复杂性。 第二步定义了一个特定的高斯消除，将解决五元和多项式多项式方程的问题分解成找到二次方程和四次方程的根的一个更简单的问题。