The class of the quadratic residue codes (QR-codes) over the ring Zopf 4  contains very good Zopf 4 -linear codes. It is well known that the Gray images of the QR-codes over Zopf 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 Zopf 4 , and applied it to all Zopf 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 Zopf 4 -linear code which is better than any known comparable linear code.
['Michael Kiermaier', 'Alfred Wassermann']
On the minimum Lee distance of quadratic residue codes over ℤ 4 4