On some classes of optimal and near-optimal polynomial codes

We generalize a recent idea for constructing codes over a finite field by evaluating a certain collection of polynomials over at elements of an extension field. We show that many codes with the best parameters presently known can be obtained by this construction. In particular, a new linear code, a [40,23,10]-code over is discovered. Moreover, several families of optimal and near-optimal codes can also be obtained by this method. We call a code near-optimal if its minimum distance is within 1 of the known upper bound.