Abstract: In present paper, we propose a construction of 1-quasi-perfect $q$-ary codes with parameters of generalized Reed-Muller codes of order $r = (q -1)m - 2$, where $m$ is a positive integer. For $q \geq 3$, $m \geq 2$, the proposed construction allows one to construct nonlinear 1-quasi-perfect $q$-ary codes with different kernel dimensions. The dimensions of the kernel of nonlinear 1-quasi-perfect $q$-ary codes constructed using the proposed construction are calculated.

Cite: Romanov A.M.
On the kernels of nonlinear quasi-perfect codes
Международная конференция "Мальцевские чтения" 10-14 Nov 2025