On some classes of optimal and near-optimal polynomial codes

AbstractWe generalize a recent idea for constructing codes over a finite field Fq by evaluating a certain collection of polynomials over Fq 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 F5 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