Complete decoding of triple-error-correcting binary BCH codes

An extensive study of binary triple-error-correcting codes of primitive length n = 2^{m} - 1 is reported that results in a complete decoding algorithm whenever the maximum coset weight W_{max} is five. In this regard it is shown that W_{max} = 5 when four divides m , and strong support is provided for the validity of the conjecture that W_{max} = 5 for all m . The coset weight distribution is determined exactly in some cases and bounded in others.