On automorphism groups of binary primitive BCH codes

It is proved that, for a given m⩾5, the automorphism group Aut(C) of a binary primitive BCH code C of length 2^m-1 with Bose distance d₀, 3⩽d₀-1<1+2[^m+3/₄], 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 d₀=2^m-1-1-2[^m/₂] and 2, 3, 4-error-correcting binary primitive BCH codes. If only legal permutations which are also linear operators on the vector space F_2(m) over F₂ are concerned, no exceptional permutations can be found even with Bose distance d₀, 1+2[ ^m+3/₄]⩽d₀-1<1+2[^m-1/ ₂]