Error Correcting Codes Associated with Complex Hadamard Matrices
Error Correcting Codes Associated with Complex Hadamard Matrices
复制标题
与复杂哈达玛矩阵相关的纠错码
DOI：
10.1016/s0893-9659(98)00059-7
复制
发表时间：
1998
影响因子：
3.7
通讯作者：
C. H. Cooke
中科院分区：
文献类型：
--
作者：
I. Heng;C. H. Cooke
对于素数p>；2，广义Hadamard矩阵H(p，pt)可以表示为H=xA，其中符号表示hij=xaij。证明了A的行向量表示p元纠错码。根据t的值，出现线性或非线性代码。码字等距且具有最小汉明距离d=(p−1)t。码可被扩展以具有长度为pt−1的N=p2t个码字。
For primes p > 2, the generalized Hadamard matrix H(p,pt) can be expressed as H = xA, where the notation means hij= xaij. It is shown that the row vectors of A represent a p-ary error correcting code. Depending upon the value of t, either linear or nonlinear codes emerge. Code words are equidistant and have minimum Hamming distance d = (p − 1)t. The code can be extended so as to possess N = p2t code words of length pt − 1.