Binary Cyclic Codes Of Length Research Articles

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

It is shown that if m \neq 8, 12 and m > 6 , there are some binary primitive BCH codes (BCH codes in a narrow sense) of length 2^{m} - 1 whose 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 even m \geq 6 , there are some binary cyclic codes of length 2^{m} - 1 that have more information digits than the primitive BCH codes of length 2^{m} - 1 with the same minimum weight.