International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 403-406
doi:10.1155/S0161171282000398
Information sets as permutation cycles for quadratic residue codes
Department of Mathematics, Boston College, Chestnut Hill, Massachusetts, USA
Received 6 August 1979; Revised 20 October 1980
Copyright © 1982 Richard A. Jenson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.