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 F q [X]/〈x m + 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.
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References
Barbier, M., Chabot, C., Quintin, G.: On quasi-cyclic codes as a generalization of cyclic codes. Finite Fields and Their Applications 18, 904–919 (2012)
Blackford, T.: Negacyclic duadic codes. Finite Fields and Their Applications 14, 930–943 (2008)
Cao, Y.: Structural properties and enumeration of 1-generator generalized quasi-cyclic codes. Designs, Codes and Cryptography 60, 67–79 (2011)
Cao, Y., Gao, J.: Constructing quasi-cyclic codes from linear algebra theory. Designs, Codes and Cryptography 67(1), 59–75 (2013)
Dinh, H.Q.: On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions. Finite Fields and Their Applications 14, 22–40 (2008)
Han, S., Kim, J.-L., Lee, H., Lee, Y.: Construction of quasi-cyclic self-dual codes. Finite Fields and Their Applications 18, 613–633 (2012)
Kamiya, N.: Quasi-Cyclic Codes from a Finite Affine Plane. Designs, Codes and Cryptography 38, 311–329 (2006)
Ling, S., Solé, P.: On the Algebraic Structure of Quasi-Cyclic Codes I: Finite Fields. IEEE Transactions on Information Theory 47(7), 2751–2760 (2001)
Solé, P., Yemen, O.: Binary quasi-cyclic codes of index 2 and skew polynomial rings. Finite Fields and Their Applications 18, 685–699 (2012)
Venkaiah, V.C., Aaron Gulliver, T.: Quasi-cyclic codes over F 13 and enumeration of defining polynomials. Journal of Discrete Algorithms 16, 249–257 (2012)
Chen Z.: (2011), http://www.tec.hkr.se/~chen/research/codes/ (accessed Septemper 2011)
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Li, X., Fu, C. (2013). Trace Representation of Quasi-negacyclic Codes. In: Liu, D., Alippi, C., Zhao, D., Hussain, A. (eds) Advances in Brain Inspired Cognitive Systems. BICS 2013. Lecture Notes in Computer Science(), vol 7888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38786-9_42
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DOI: https://doi.org/10.1007/978-3-642-38786-9_42
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