A simple decoding algorithm for the [24,12,8] extended Golay code

A simple high-speed decoding algorithm for the [24,12,8] extended Golay code, based on the |a+x| b+x|a+b+x| Turyn construction is described. The algorithm can be easily realized in combinational circuits. Futhermore we show that [24,12,8] Golay code can correct simultaneously all patterns of three or fewer random errors as well as certain patterns of quadruple errors such as 4-bit cyclic single-burst and two-dimensional byte errors.