Abstract
It is proved that, for a given m ≥ 5, the automorphism group Aut(C) of a binary primitive BCH code C of length 2 <sup>m</sup> - 1 with Bose distance d <sub>0</sub> , 3 ≤ d <sub>0</sub> - 1 < 1 + 2 <sup>[m+3/4]</sup> , consists of only traditional permutations. Automorphism groups of several classes of binary primitive BCH codes are determined. These include binary primitive BCH codes with Bose distance d <sub>0</sub> = 2 <sup>m-1</sup> - 1 - 2 <sup>[m/2]</sup> and 2, 3, 4-error-correcting binary primitive BCH codes. If only legal permutations which are also linear operators on the vector space F <sub>2(m)</sub> over F <sub>2</sub> are concerned, no exceptional permutations can be found even with Bose distance d <sub>0</sub> , 1 + 2 <sup>[m+3/4]</sup> ≤ d <sub>0</sub> - 1 < 1 + 2 <sup>[m-1/2]</sup> .