Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes

It is shown that ifm neq 8, 12andm > 6, there are some binary primitive BCH codes (BCH codes in a narrow sense) of length2^{m} - 1whose minimum weight is greater than the BCH bound. This gives a negative answer to the question posed by Peterson 1] of whether or not the BCH bound is always the actual minimum weight of a binary primitive BCH code. It is also shown that for any evenm geq 6, there are some binary cyclic codes of length2^{m} - 1that have more information digits than the primitive BCH codes of length2^{m} - 1with the same minimum weight.