Good Linear Codes from Polynomial Evaluations

In the present paper, we generalize the ideas of code constructions from our previous papers . It turns out that the codes in the previous papers can be viewed as special cases of those in this paper. Moreover, our constructions produce some good codes in terms of their parameters. In particular, some best-known codes can be obtained through our methods. Furthermore, our constructions are explicit and the codes can be easily implemented as shown in the tables of Appendix. Besides, one new code, i.e., a 4-ary [64,15,31]-linear code, is found through our constructions.