Novel Algebraic Structure for Cyclic Codes
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.
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- 1.Prange, E.: Cyclic Error-Correcting Codes in Two Symbols. Electronics Research Directorate, Air Force Cambridge Res. Ctr. (1957)Google Scholar
- 2.MacWilliams, F.J., Sloane, N.J.A: The Theory of Error-Correcting Code. North-Holland, Amsterdam (1977)Google Scholar
- 4.Blahut, R.E.: Theory and Practice of Error Control Coding. Addison-Wesley, Reading, MA (1983)Google Scholar
- 5.Moon, T.K.: Error Correction Coding: Mathematical Methods and Algorithm. John Wiley & Sons, Inc., Chichester (2005)Google Scholar
- 9.Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications, 2nd edn. Cambridge Univ. Press, Cambridge (1997)Google Scholar