论文标题
通过2级自相关序列和置换多项式的互补序列集的结构和完整的互补代码
Constructions of complementary sequence sets and complete complementary codes by 2-level autocorrelation sequences and permutation polynomials
论文作者
论文摘要
在本文中，深入研究了一种构建互补序列集和完整互补代码的方法。通过考虑Hadamard矩阵的代数结构，我们的主要结果决定了所谓的$δ$ - 线性项和$δ$ - 二次的项。首先，将$ p $ -ary（$ p $ prime）序列的Golay互补套件和Kasami等人的广义芦苇架代码联系起来的强大理论。已开发。这些代码具有良好的错误纠正功能，严格控制的PMEPR，并使用$ p^n $ subcarriers大大扩展了OFDM应用程序的编码选项范围。另一个结果，我们在CSS和CCC中的序列与具有2级自相关，痕量函数和置换多项式（PP）的序列之间建立了先前未认识到的连接。
In this paper, a recent method to construct complementary sequence sets and complete complementary codes by Hadamard matrices is deeply studied. By taking the algebraic structure of Hadamard matrices into consideration, our main result determine the so-called $δ$-linear terms and $δ$-quadratic terms. As a first consequence, a powerful theory linking Golay complementary sets of $p$-ary ($p$ prime) sequences and the generalized Reed-Muller codes by Kasami et al. is developed. These codes enjoy good error-correcting capability, tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using $p^n$ subcarriers. As another consequence, we make a previously unrecognized connection between the sequences in CSSs and CCCs and the sequence with 2-level autocorrelation, trace function and permutation polynomial (PP) over the finite fields.
