2019/06/13 by Liqin Qian, Qian, Liqin, Xiwang Cao +5
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1906.05523
openalex publication_date 2019/06/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
In this paper, we present explicit description on the additive characters, multiplicative characters and Gauss sums over a local ring. As an application, based on the additive characters and multiplicative characters satisfying certain conditions, two new constructions of complex codebooks over a local ring are introduced. With these two constructions, we obtain two families of codebooks achieving asymptotically optimal with respect to the Welch bound. It's worth mentioning that the codebooks constructed in this paper have new parameters.