On automorphism groups of binary primitive BCH codes

It is proved that, for a given m/spl ges/5, the automorphism group Aut(C) of a binary primitive BCH code C of length 2/sup m/-1 with Bose distance d/sub 0/, 3/spl les/d/sub 0/-1<1+2[/sup m+3///sub 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 d/sub 0/=2/sup m-1/-1-2[/sup m///sub 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/sub 2(m)/ over F/sub 2/ are concerned, no exceptional permutations can be found even with Bose distance d/sub 0/, 1+2[/sup m+3///sub 4/]/spl les/d/sub 0/-1<1+2[/sup m-1///sub 2/].<
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