1. On the Construction of Some Optimal Polynomial Codes.
- Author
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Yue Hao, Jiming Liu, Yu-Ping Wang, Yiu-ming Cheung, Hujun Yin, Licheng Jiao, Jianfeng Ma, Yong-Chang Jiao, Yajing Li, and Weihong Chen
- Abstract
We generalize the idea of constructing codes over a finite field Fq 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 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. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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