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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Li, Y., Chen, W. (2005). On the Construction of Some Optimal Polynomial Codes. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596981_11
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DOI: https://doi.org/10.1007/11596981_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30819-5
Online ISBN: 978-3-540-31598-8
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