Advances in the merit factor problem for binary sequences
Advances in the merit factor problem for binary sequences
复制标题
二元序列优值因子问题的进展
DOI：
10.1016/j.jcta.2013.01.010
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
K. Schmidt
中科院分区：
文献类型：
--
作者：
J. Jedwab;D. Katz;K. Schmidt
具有大优值因子（小均方非周期自相关）的二进制序列的识别是复杂分析和组合优化的一个老问题，在数字通信工程和凝聚态物理中具有实际意义。我们建立了几个二元序列族的渐近优值因子，从而证明了各种猜想，解释了其他作者提出的数值证据，并将以前以分散形式出现的结果汇集在一个框架内。我们首次展示了斜对称序列族，其渐近优值因子与所有二元序列的已知值（大于 6.34 的代数数）一样大；鉴于戈莱的猜想，即斜对称序列的子类具有渐近最优优值因子，这一点很有趣。我们的方法结合了傅立叶分析、特征和估计以及多面体格点数估计。
The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications engineering and condensed matter physics. We establish the asymptotic merit factor of several families of binary sequences and thereby prove various conjectures, explain numerical evidence presented by other authors, and bring together within a single framework results previously appearing in scattered form. We exhibit, for the first time, families of skew-symmetric sequences whose asymptotic merit factor is as large as the best known value (an algebraic number greater than 6.34) for all binary sequences; this is interesting in light of Golayʼs conjecture that the subclass of skew-symmetric sequences has asymptotically optimal merit factor. Our methods combine Fourier analysis, estimation of character sums, and estimation of the number of lattice points in polyhedra.