Golay encoding/decoding via BCH-Hamming

The (24, 12;8) extended Golay Code can be generated as a 6 × 4 binary matrix from the (15, 11;3) BCH-Hamming Code, represented as a 5 × 3 matrix, by adding a row and column, both of odd or even parity. The odd parity case provides the additional 12th dimension. Furthermore, any three columns and five rows of the 6 × 4 Golay form a permuted BCH- Hamming (15, 11;3) Code. Using the single-error correction of the BCH-Hamming Code, it is possible to decode in a primitive combinatoric fashion all three error patterns. Single- and double-error correction is almost immediate.