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