On the construction of some optimal polynomial codes

Abstract

We generalize the idea of constructing codes over a finite field F q by evaluating a certain collection of polynomials at elements of an extension field of Fq. Our approach for extensions of arbitrary degrees is different from the method in [3]. We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between Fq and Fqt denoted by Fqs where s divides t. It turns out that many codes with the best parameters can be obtained by our construction and improve the parameters of Brouwer's table [1]. Some codes we get are optimal by the Griesmer bound. © Springer-Verlag Berlin Heidelberg 2005.