# On the Construction of Some Optimal Polynomial Codes

• Yajing Li
• Weihong Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3802)

## 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 F q . 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 F q and F $$_{q^{t}}$$ denoted by F $$_{q^{s}}$$ 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.

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