On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order

We study theoretically conditions of correct operation of a new soft decisions decoder of Reed–Muller second order codes over the field $\mathbb F_3$, whose experimental research showed that its corrective ability exceeds that of the decoder of the minimum Hamming's distance. For discrete data channel allocated we indicated the smoothness condition under which the decoder guarantees correction of all errors, the number of which does not exceed the permissible number of errors referred to the code design.