Methods and apparatus are provided for reading and writing data in q-level cells of solid-state memory, where q>2. Input data is encoded into codewords having N qary symbols, wherein the symbols of each codeword satisfy a single-parity-check condition. Each symbol is written in a respective cell of the solid state memory by setting the cell to a level dependent on the qary value of the symbol. Memory cells are read to obtain read signals corresponding to respective codewords. The codewords corresponding to respective read signals are detected by relating the read signals to a predetermined set of N-symbol vectors of one of which each possible codeword is a permutation.