I don't know a ton about chemistry, but I think you may be mistaken here ... sodium chlrITE is made by reducing Sodium Chlorate. I don't think that it can be be made from table salt , but I may be wrong.
"Sodium chlorite is derived indirectly from sodium chlorate, NaClO3. First, the explosively unstable gas chlorine dioxide, ClO2 is produced by reducing sodium chlorate in a strong acid solution with a suitable reducing agent (for example, sodium chloride, sulfur dioxide, or hydrochloric acid). The chlorine dioxide is then absorbed into an alkaline solution and reduced with hydrogen peroxide, H2O2 (Hydrogen-Peroxid) yielding sodium chlorite."