Trace representation of quasi-negacyclic codes

Authors:
Xiuli Li;Chenghua Fu
Affiliations:
School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China;School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China
Venue:
BICS'13 Proceedings of the 6th international conference on Advances in Brain Inspired Cognitive Systems
Year:
2013

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Abstract

The alphabet decomposition of quasi-negacyclic codes is developed. By the use of the Chinese Remainder Theorem (CRT), or of the Discrete Fourier Transform (DFT), the ring Fq[X]/〈xm+1 〉 can be decomposed into a direct product of fields. The trace representation for quasi-negacyclic codes generalizes nicely the trace representation of cyclic and quasi-cyclic codes. Furthermore quasi-negacyclic codes are constructed by Vandermonde matrices.