Title :
No binary quadratic residue code of length 8m-1 is quasi-perfect
Author :
Chen, Xuemin ; Reed, I.S. ; Truong, T.K.
Author_Institution :
Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA
fDate :
3/1/1994 12:00:00 AM
Abstract :
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
Keywords :
Hamming codes; error correction codes; (23,12,7) Golay code; (7,4,3) Hamming code; QR codes; binary quadratic residue code; binary self-dual codes; length 8m-1; quasiperfect QR codes; Binary codes; Information theory; Linear code; Upper bound; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
