To the Times
To the Times
复制标题
致时代
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Andrew Booth
中科院分区：
文献类型：
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作者：
Andrew Booth
q 阶有限域上的广义权重矩阵、Bhaskar-Rao 设计和广义 Hadamard 矩阵用于构造自正交线性码。某些最小秩矩阵会产生最佳代码。在 q = 4 的特殊情况下，代码产生量子纠错码。从广义称重矩阵导出的自正交码 – p. 11 2/16 广义加权矩阵 g 阶乘法群 G 上的广义加权矩阵是一个 v × b 矩阵 M = (mij)，其条目来自 G ∪ {0}，使得对于每两行 (mi1, . . . ,mib), (mj1, . . . ,mjb)，i 6= j，多集 {mism −1 js | 1 ≤ s ≤ b, mjs 6= 0} (1) 包含 G 中每个元素的次数相同。从广义称重矩阵导出的自正交码 – p. 11 3/16
Generalized weighing matrices, Bhaskar-Rao designs, and generalized Hadamard matrices over a finite field of order q are used for the construction of self-orthogonal linear codes. Certain matrices of minimum rank yield optimal codes. In the special case when q = 4, the codes yield quantum error-correcting codes. Self-orthogonal Codes Derived from Generalized Weighing Matrices – p. 2/16 Generalized Weighing Matrices A generalized weighing matrix over a multiplicative group G of order g is a v × b matrix M = (mij) with entries from G ∪ {0} such that for every two rows (mi1, . . . ,mib), (mj1, . . . ,mjb), i 6= j, the multi-set {mism −1 js | 1 ≤ s ≤ b, mjs 6= 0} (1) contains every element of G the same number of times. Self-orthogonal Codes Derived from Generalized Weighing Matrices – p. 3/16