Abstract
The novel algebraic structure for the cyclic codes, Cyclic Multiplicative Groups (CMGs) over polynomial ring, is proposed in this paper. According to this algorithm, traditional cyclic codes can be considered as a subclass in these cyclic codes. With CMGs structure, more plentiful good cyclic code cosets can be found in any polynomial rings than other methods. An arbitrary polynomial in polynomial ring can generate cyclic codes in which length of codewords depend on order of the polynomial. Another advantage of this method is that a longer code can be generated from a smaller polynomial ring. Moreover, our technique is flexibly and easily implemented in term of encoding as well as decoding. As a result, the CMGs can contribute a new point of view in coding theory. The significant advantages of proposed cyclic code cosets can be applicable in the modern communication systems and crypto-systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Prange, E.: Cyclic Error-Correcting Codes in Two Symbols. Electronics Research Directorate, Air Force Cambridge Res. Ctr. (1957)
MacWilliams, F.J., Sloane, N.J.A: The Theory of Error-Correcting Code. North-Holland, Amsterdam (1977)
Van Lint, J.H.: Introduction to Coding Theory, 3rd edn. Springer, Heidelberg (1999)
Blahut, R.E.: Theory and Practice of Error Control Coding. Addison-Wesley, Reading, MA (1983)
Moon, T.K.: Error Correction Coding: Mathematical Methods and Algorithm. John Wiley & Sons, Inc., Chichester (2005)
Pincin, A.: A New Algorithm for Multiplication in Finite Fields. IEEE Trans. Computer 38(1), 1045–1049 (1989)
Namin, A.H., Wu, H., Ahmadi, M.: Comb Architectures for Finite Field Multiplication in F_2m. IEEE Trans. Computers 56(7), 909–916 (2007)
Katti, R., Brennan, J.: Low Complexity Multiplication in a Finite Field Using Ring Representation. IEEE Trans. Computers 52(4), 418–427 (2003)
Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications, 2nd edn. Cambridge Univ. Press, Cambridge (1997)
Wang, C.C., Truong, T.K., Shao, H.M., Deutsch, L.J., Omura, J.K., Reed, I.S.: VLSI Architectures for Computing Multiplications and Inverses in GF(2m). IEEE Trans. Computers 34(8), 709–717 (1985)
Wu, H., Hasan, M.A., Blake, I.F., Gao, S.: Finite Field Multiplier Using Redundant Representation. IEEE Trans. Computers 51(11), 1306–1316 (2002)
Baodian, W., Liu, D., Ma, W., Wang, X.: Property of Finite Fields and Its Cryptography Application. Electron. Lett. 39, 655–656 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bac, D.H., Binh, N., Quynh, N.X. (2007). Novel Algebraic Structure for Cyclic Codes. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-77224-8_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77223-1
Online ISBN: 978-3-540-77224-8
eBook Packages: Computer ScienceComputer Science (R0)