Title :
On the minimum Lee distance of quadratic residue codes over ℤ44
Author :
Kiermaier, Michael ; Wassermann, Alfred
Author_Institution :
Math. Dept., Univ. of Bayreuth, Bayreuth
Abstract :
The class of the quadratic residue codes (QR-codes) over the ring Zopf4 contains very good Zopf4-linear codes. It is well known that the Gray images of the QR-codes over Zopf4 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 Zopf4, and applied it to all Zopf4-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 Zopf4-linear code which is better than any known comparable linear code.
Keywords :
Gray codes; Hamming codes; binary codes; linear codes; Gray images; Zopf4-linear codes; higher minimum Hamming distance; minimum Lee distance; nonlinear binary codes; quadratic residue codes; Algebra; Binary codes; Block codes; Code standards; Documentation; Hamming distance; Internet; Linear code; Parity check codes; Zinc;
Conference_Titel :
Information Theory, 2008. ISIT 2008. IEEE International Symposium on
Conference_Location :
Toronto, ON
Print_ISBN :
978-1-4244-2256-2
Electronic_ISBN :
978-1-4244-2257-9
DOI :
10.1109/ISIT.2008.4595465
