On the minimum Lee distance of quadratic residue codes over ℤ₄

Titelangaben

Kiermaier, Michael ; Wassermann, Alfred:
On the minimum Lee distance of quadratic residue codes over ℤ₄.
In: 2008 IEEE International Symposium on Information Theory proceedings. - Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE) , 2008 . - S. 2617-2619
ISBN 978-1-4244-2256-2
DOI: https://doi.org/10.1109/ISIT.2008.4595465

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Abstract

The class of the quadratic residue codes (QR-codes) over the ring ℤ₄ contains very good ℤ₄-linear codes. It is well known that the Gray images of the QR-codes over ℤ₄ 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 ℤ₄, and applied it to all ℤ₄-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 ℤ₄-linear code which is better than any known comparable linear code.