A class of generalized cyclic codes

In this paper, we discuss how to construct a class of generalized cyclic codes, denoted by GCC. It is well known that 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. Similarly the construction of cyclic codes, we explain how g(x) can generate a GCC. Meanwhile, as related to cyclic codes, experiments show that GCC can always produce a better parameter and/or give more linear codes. On the basis the of concept of GCC, we can also construct a linear code of 90,76,5] _2.