On Reed-Solomon Codes |
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Authors: | Qunying LIAO |
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Affiliation: | Institution of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China |
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Abstract: | The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small. In the first part, the result of Li and Wan is improved. On the other hand, one of the important parameters of an error-correcting code is the dimension. In most cases, one can only get bounds for the dimension. In the second part, a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained. |
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Keywords: | Reed-Solomon code Weil bound Error distance Rational function Trace Reed-Solomon code Trace map |
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