论文标题
具有高功绩因子的新类二进制序列
New Classes of Binary Sequences with High Merit Factor
论文作者
论文摘要
Golay在1972年首次引入了优点因素（MF）度量。拥有大量MF值的序列对丰富的学科清单非常有趣 - 从物理和化学到数字通信，信号处理和密码学。在过去的半个世纪中，提出了用于查找此类序列的歧管方法和策略。 Golay被称为最困难的优化问题之一，他写道这是一个“具有挑战性和迷人的问题”。他关于这个问题的出版物跨越了20多年。 Golay本人引入了一种有益的序列，称为偏度对称序列，或具有奇数长度的有限二进制序列，其替代自相关值等于0。它们的筛分结构大大降低了寻找具有奇数长度和高MF的二进制序列的计算工作。考虑到这一点，文献中要找到的大多数论文仅集中在此类上，而是更喜欢它们，而不是长度均匀的二进制序列。在这项工作中，提出了一类新的有限二进制序列，具有等于1的备用自相关绝对值的均匀长度。我们表明，新类的MF值与偏斜序列的相邻类别的MF值密切相关。我们进一步使用分区数问题和电势概念引入了新的序列子类，该序列通过辅助三元序列衡量。在我们的整个实验中，发现了小于225的二进制序列的MF记录，所有长度大于225。现在透露了各个长度的二进制序列，奇数甚至不到$ 2^8 $，并带有MF $> 8 $，以及所有长度，奇数甚至少于$ 2^9 $，并以MF $> 7 $的价格透露。
The Merit Factor (MF) measure was first introduced by Golay in 1972. Sequences possessing large values of MF are of great interest to a rich list of disciplines - from physics and chemistry to digital communications, signal processing, and cryptography. Throughout the last half-century, manifold approaches and strategies were proposed for finding such sequences. Referenced as one of the most difficult optimization problems, Golay wrote that it is a "challenging and charming problem". His publications on this problem spanned more than 20 years. Golay himself introduced one beneficial class of sequences, called skew-symmetric sequences, or finite binary sequences with odd lengths with alternate autocorrelation values equal to 0. Their sieving construction greatly reduces the computational efforts of finding binary sequences with odd lengths and high MF. Having this in mind, the majority of papers to be found in the literature are focused solely on this class, preferring them over binary sequences with even lengths. In this work, a new class of finite binary sequences with even lengths with alternate autocorrelation absolute values equal to 1 is presented. We show that the MF values of the new class are closely related to the MF values of adjacent classes of skew-symmetric sequences. We further introduce new sub-classes of sequences using the partition number problem and the notion of potentials, measured by helper ternary sequences. Throughout our experiments, MF records for binary sequences with many lengths less than 225, and all lengths greater than 225, are discovered. Binary sequences of all lengths, odd or even, less than $2^8$ and with MF $>8$, and all lengths, odd or even, less than $2^9$ and with MF $>7$, are now revealed.
