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五、BCH码的一些几何原理 对BCH码来说,有用的是向量几何和m维q元域上的投影几何(projective geometry),记为PG(m,q)和仿射几何或欧几里得几何(Euclidean geometry),记为EG(m,q)。用得最多的三维二元域GF(2)上欧几里得几何EG(3,2)。在三维空间中,任一矢量必定有三个实数x,y,z与之相对应;反之,任意三个实数,也必定有与之相对应的一个矢量。同样,设想在n维空间里,任一矢量必定有n个实数与之相对应;反之任一组n个的实数,也必有一个n维矢与之相对应,因而将这n个实数称为n维矢。如果代表一个n维矢的n个实数,是能够运算自封的有限域中的一些数,例如二元域GF(2)上的0,1两个数,则这个概念仍然成立。例如取0100表某一矢量,而1010则表另一矢量等。
V. Some Geometric Principles of BCH Codes For BCH codes, it is useful to consider the projective geometry of vector geometry and m-dimensional q-prime fields, denoted PG (m, q) and affine geometry or Euclidean Euclidean geometry, denoted as EG (m, q). The Euclidean geometry EG (3,2) on the most used three-dimensional binary field GF (2). In three-dimensional space, any vector must have three real numbers x, y, z corresponding to it; on the contrary, any three real numbers must also have a corresponding vector. Similarly, imagine that in n-dimensional space, any vector must have n real numbers corresponding to it. On the contrary, any real group of n numbers must have an n-dimensional vector corresponding to it. Therefore, For n-dimensional vector. If we represent n real numbers of a n-dimensional vector, we can compute some numbers in a self-enclosed finite field, for example, two numbers 0 and 1 on the binary field GF (2), then the concept holds. For example, take a 0100 list of a vector, and 1010 is another vector table.