Information sets as permutation cycles for quadratic residue codes

Abstract

The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1,   (p+1)/2] extended binary quadratic residue code, O(p), properly contains PSL(2,p). These codes have some of their information sets represented as permutation cycles from Aut(Q(p)). Analysis proves that all information sets of Q(7) are so represented but those of Q(23) are not.