Extended Cyclic Codes Sandwiched Between Reed-Muller Codes
Information Theory
2023-05-16 v5 math.IT
Abstract
The famous Barnes-Wall lattices can be obtained by applying Construction D to a chain of Reed-Muller codes. By applying Construction to a chain of extended cyclic codes sandwiched between Reed-Muller codes, Hu and Nebe (J. London Math. Soc. (2) 101 (2020) 1068-1089) constructed new series of universally strongly perfect lattices sandwiched between Barnes-Wall lattices. In this paper, we first extend their construction to generalized Reed-Muller codes, and then explicitly determine the minimum vectors of those new sandwiched Reed-Muller codes for some special cases.
Cite
@article{arxiv.2105.13827,
title = {Extended Cyclic Codes Sandwiched Between Reed-Muller Codes},
author = {Yan Xu and Changjiang Ji and Ran Tao and Sihuang Hu},
journal= {arXiv preprint arXiv:2105.13827},
year = {2023}
}
Comments
17 pages; several examples added