On intersection property of Reed – Muller like codes
F. I. Solov’eva · 2021 International Conference Automatics and Informatics (ICAI) · 2021
A self-complementary code having parameters of the binary linear Reed – Muller code is called a Reed – Muller like code. It is denoted $LRM_{r,m}$ (briefly LRM code if we do not specify parameters). The class of such codes contains a rich family of LRM codes obtained by the Pulatov construction. The intersection problem of such codes is investigated in the paper. We establish the existence of two LRM codes of order r having length 2mwith intersection of size $2k_{1}k_{2},1\leq k_{s}\leq|RM_{r-1,m-1}|,s=1,2$ for any $m, m\geq 4$.