Inverse Quasi Cyclic Code and Application in Chain Ring
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Keywords:
Chain Rings, Linear Codes, Cyclic Codes, Quasi-Cyclic Codes, Gray MapAbstract
The existence of inverse quasi-cyclic codes in the 2 2
u + F F ring is presented. Here, Gray
transform and inverse quasi cyclic code definitions are given first. Afterwards, its relationship with
automorphism and cyclic codes is mentioned. The proposition including Nechaev permutation, quasi
cyclic codes and Gray transformation is explained. From this it is concluded that inverse quasi cyclic
codes correspond to Gray images of the cyclic code. Finally, a 4-length repeat code example is included
regarding this topic.
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References
F.J. MacWilliams , NJA Sloane, The Theory of Error
Correcting Codes,North -Holland Publishing Company,
J. Wolfmann, Negacyclic and cyclic codes over 4
Z ,
IEEE Trans. Inf. Theory, Vol. 45, 2527-2532, 1999.
A. Bonnecaze and P. Udaya, Cyclic codes and self dual
codes 2 2
u + F F , IEEE Trans. Inf. Theory, Vol. 45, 1250
,1999.
S. Ling, C. Xing, A First Course in Coding Theory,
Cambridge University Press, 2004.
J. Qian, L., Zhang and S. Zhu, _ ) 1 ( u + cyclic and cyclic
codes over the ring 2 2
u + F F , App. Mathematics Letters,
Vol. 19, 820-823, 2006.
D. Boucher, W. Geiselmann and F. Ulmer, Skew-Cyclic
Codes , Applicable Algebra in Eng., Com. and Comp. , Vol.
, 379-389, 2007.
M.C.V. Amarra and F.R. Nemenzo, On _ ) 1 ( u − cyclic
codes over k k p p
uIF IF + ,App. Mathematics
Letters,21,1129-1133,2008.
