负周期Golay对与Hadamard矩阵
Negaperiodic Golay pairs and Hadamard matrices
摘要：
除了普通的和周期的Golay对，我们还定义了负周期的Golay对。(They第一次发生，在一个不同的名称，在一个文件伊藤。如果Hadamard矩阵也是Toeplitz矩阵，我们证明了它必须是循环的或非循环的。我们研究了由两个负循环块（2N型）构造Hadamard（和加权矩阵）。2N型Hadamard矩阵等价于负周期Golay对。我们表明，Turyn乘法的Golay对扩展到一个更一般的乘法：可以乘以Golay对长度$g$和negativepiodic Golay对长度$v$，以获得negativepiodic Golay对长度$gv$。证明了伊藤关于Hadamard矩阵的猜想等价于关于所有偶数长度的负周期Golay对存在的猜想。
英文摘要：
Apart from the ordinary and the periodic Golay pairs, we define also the negaperiodic Golay pairs. (They occurred first, under a different name, in a paper of Ito.) If a Hadamard matrix is also a Toeplitz matrix, we show that it must be either cyclic or negacyclic. We investigate the construction of Hadamard (and weighing matrices) from two negacyclic blocks (2N-type). The Hadamard matrices of 2N-type are equivalent to negaperiodic Golay pairs. We show that the Turyn multiplication of Golay pairs extends to a more general multiplication: one can multiply Golay pairs of length $g$ and negaperiodic Golay pairs of length $v$ to obtain negaperiodic Golay pairs of length $gv$. We show that the Ito's conjecture about Hadamard matrices is equivalent to the conjecture that negaperiodic Golay pairs exist for all even lengths.
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