Title data
Kiermaier, Michael ; Wassermann, Alfred:
Minimum weights and weight enumerators of ℤ₄linear quadratic residue codes.
In: IEEE Transactions on Information Theory.
Vol. 58
(July 2012)
Issue 7
.
 pp. 48704883.
ISSN 00189448
DOI: https://doi.org/10.1109/TIT.2012.2191389
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
A fast method to compute the minimum Lee weight and the symmetrized weight enumerator of extended quadratic residue codes (XQRcodes) over the ring ℤ₄ is developed. Our approach is based on the classical BrouwerZimmermann algorithm and additionally takes advantage of the large group of automorphisms and the selfduality of the ℤ₄linear XQRcodes as well as the projection to the binary XQRcodes.
As a result, the hitherto unknown minimum Lee distances of all ℤ₄linear XQRcodes of lengths between 72 and 104 and the minimum Euclidean distances for the lengths 72, 80, and 104 are computed. It turns out that the binary Gray image of the ℤ₄linear XQRcodes of lengths 80 and 104 has higher minimum distance than any known linear binary code of equal length and cardinality. Furthermore, the ℤ₄linear XQRcode of length 80 is a new example of an extremal ℤ₄linear type II code. Additionally, we give the symmetrized weight enumerator of the ℤ₄linear XQRcodes of lengths 72 and 80, and we correct the weight enumerators of the ℤ₄linear XQRcode of length 48 given by Pless and Qian and Bennecaze et al.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Institutions of the University:  Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics and Didactics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  20 Nov 2014 08:24 
Last Modified:  20 Nov 2014 08:24 
URI:  https://eref.unibayreuth.de/id/eprint/3730 