No binary quadratic residue code of length 8m-1 is quasi-perfect
Xuemin Chen, I.S. Reed, Trieu‐Kien Truong · IEEE Transactions on Information Theory · 1994
The class of binary quadratic residue (QR) codes of length n=8m-1 contains two perfect codes. These are the (7,4,3) Hamming code and the (23,12,7) Golay code. However, it is proved in the present paper that there are no quasi-perfect QR codes of length 8m-1. Finally, this result is generalized to all binary self-dual codes of length N>72.>