@article{Alahmadi2023, 
author = {Adel Alahmadi and Altaf Alshuhail and Alaa Altassan and Hatoon Shoaib and Patrick Solé},
title = {Double circulant codes for the Lee and Euclidean distance},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {23566-23577},
keywords = {double circulant codes, Lee distance, Euclidean distance, spherical codes, deletion codes},
url = {https://www.sciopen.com/article/10.3934/math.20231198},
doi = {10.3934/math.20231198},
abstract = {This paper investigates double circulant codes of length    2  n over              Z                                            p            m                               where    p is an odd prime,    n goes to infinity, and    m  ≥  1 is a fixed integer. Using random coding, we obtain families of asymptotically good Lee codes over              Z                                            p            m                               in the case of small and large alphabets, and asymptotically good Euclidean codes over              Z                                            p            m                               for small alphabets. We use Euclidean codes to construct spherical codes, and Lee codes to construct insertion/deletion codes, by a projection technique due to (Yaglom, 1958) for spherical codes, and to (Sok et al., 2018) for deletion codes.}
}