Constructor Of A Class Of Linear Codes

How to construct good codes is a basic problem in coding theory. In this paper, we mainly discuss the constructions of a class of AG codes (generalized Reed-Solomon codes).The generalized Reed-Solomon codes over the finite field F_q aremaximum-distance separable (MDS) codes. This class of codes has optimal parameters. However, the length of such a code is at most q. San Ling and Chaoping Xing haveconstructed a class of linear codes with elements of F_q~2 in [11]. And they got somecodes with better parameters, In [12], San Ling, Harald Niederreiter and Chaoping Xing have constructed a kind of linear codes using elements from any finite extension F_q~s(s≥3) of F_q. The rational functions are linearly combinations of the product ofsymmetric polynomial power. The lengths of codes constructed in this way are arbitrarily large. Here, I want to construct a class of linear codes still over any finite extension F_q~s(s≥3) of F_q. But I use the approach as in [13] extending [14] not as in[12]. It is easy to prove that the class of linear codes constructed in this paper is equivalent to the ones in [12].