Character sums over a non-chain ring and their applications
Character sums over a non-chain ring and their applications
复制标题
DOI：
10.3934/amc.2020134
复制
发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Liqin Qian;X. Cao
中科院分区：
文献类型：
--
作者：
Liqin Qian;X. Cao
环上的一些有价值的结果在编码理论和纠错码理论中具有很好的应用前景。本文研究了非链环上的特征和及其在码本中的应用。这项研究有两个主要因素。第一部分是研究非链环上的高斯和、超爱森斯坦和、雅可比和，并研究这些特征和的性质。对于它们的应用，第二部分是给出三类关于Welch界的渐近最优码本和一类关于Levenshtein界的最优码本，它们是由非链环上的字符和构造的。
Some valuable results over rings have a promising utilization in coding theory and error-correcting code theory. In this paper, we study character sums over a certain non-chain ring and their applications in codebooks. There are two major ingredients in this study. The first ingredient is to investigate Gaussian sums, hyper Eisenstein sums, Jacobi sums over a certain non-chain ring and study the properties of these character sums. For their applications, the second ingredient is to present three classes of asymptotically optimal codebooks with respect to the Welch bound and a family of optimal codebooks with respect to the Levenshtein bound, which are constructed from character sums over a certain non-chain ring.