On the minimum Lee distance of quadratic residue codes over Z4
Michael Kiermaier ; Alfred Wassermann ;
07/2008, Toronto, IEEE, ISBN/ISSN/ISMV Nummer:978-1-4244-2571-6
in: Proceedings of the International Symposium on Information Theory (ISIT), 2008. Doi-Nummer:
The class of the quadratic residue codes (QR-codes) over the ring Z_4 contains very good Z_4-linear codes. It is well known that the Gray images of the QR-codes over Z_4 of length 8, 32 and 48 are non-linear binary codes of higher minimum Hamming distance than comparable known linear codes. The QR-Code of length 48 is also the largest one whose exact minimum Lee distance was known. We developed a fast algorithm to compute the minimum Lee distance of QR-codes over Z_4, and applied it to all Z_4-linear QR-codes up to length 98. The QR-code of length 80 has minimum Lee distance 26. Thus it is a new example of a Z_4-linear code which is better than any known comparable linear code.