ACTA Mathematicae Applicatae Sinica (English Series)
Vol. 16, No. 1, pp 53 -- 58, (2000)


                A Class of Generalized Cyclic Codes

                                 By
                     Zhuojun Liu and Dongdai Lin
                     {zliu,ddlin}@mmrc.iss.ac.cn

               Institute of Systems Science, Academia Sinica
                     Beijing 100080, P. R.  China

Abstract   -----  In this paper, we discuss how  to  construct a class of 
generalized cyclic codes, which  is  denoted  by  GCC. It is well known a 
cyclic code is  generated  by  a  factor  of  x^n - 1. Clearly, any monic 
polynomial g(x) with degree  less  than n could be considered as a factor 
of some polynomial  of  degree n. Similar with the construction of cyslic 
codes, we explain how  g(x) can generate a GCC. We will show the encoding 
procedure  for  GCC is the same to a cyclic code's. Meanwhile, relatively 
to cyclic codes, GCC can always produce better parameter and/or give more 
linear codes.


Keywords  Cyclic Code, Error-Correcting Cede, Generating Polynomials,
          Generating Matrix


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Full paper available upon request