BCH question,decoding error occurs when err number is (t,2t]

No. A BCH code can EITHER correct t errors OR detect 2t errors. Not both.

Vladimir Vassilevsky DSP and Mixed Signal Design Consultant

I think the point that the OP is missing is that *beyond* 2t (or t, depending on whether you are looking for detection or correction, respectively), the algorithm gives *incorrect* answers.

Put it in perspective:

Simple parity can detect a one bit error. OTOH, if you have *two* errors, parity reports *none*. I.e., the "parity algorithm" gives incorrect results if the number of errors doesn't fit within its intended scope.

When choosing an ECC algorithm, you have to understand what types of errors are *likely* to occur in your data.

E.g., data recorded on a "CD" is likely to encounter errors that are physically adjacent (i.e., a scratch on the medium) moreso than in large *bursts*.

OTOH, a data communications channel is more likely to encounter errors that are adjacent in *time* (as a dropout or a burst of noise interrupts the communications).

Pick the wrong approach and you will not only fail to get the error detect/correct behavior that you desire but, the algorithm can actually make matters *worse*.

HTH