Extended Cyclic Codes Sandwiched Between Reed-Muller Codes
arXiv:2105.13827 · doi:10.1109/TIT.2022.3202341
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.
17 pages; several examples added