j******d
发帖数: 70 | 1 偶不是学数学的,在看 a course in error correcting codes, p6 的Varchamov-Gilbert
bound 的证明实在是不理解.
there exists a binary linear code of length $n$, with at most $m$ linearly
independent parity checks and minimum distance at least $d$, if
\sum_{k=0}^{d-2}\binom{n-1}{k}<2^m
证明:建立一个 m*n 矩阵,其中任意 n-1 列 independent.第一列可以是任意非0的m位二
进制向量.now suppose we have chosen $i$ columns so that no $d-1$ are linearly
dependent. there are
c(i,1)+c(i,2)+...+c(i,d-2) lieaner combinations of these columns taken $d-2$
or fewer at a t |
|
