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| On Reed-Solomon Codes |
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Citation： |
Qunying LIAO.On Reed-Solomon Codes[J].Chinese Annals of Mathematics B,2011,32(1):89~98 |
| Page view： 1861
Net amount： 1632 |
Authors： |
Qunying LIAO; |
Foundation： |
the National Natural Science Foundation of China (No. 10990011), the Doctoral
Program Foundation of Ministry of Education of China (No. 20095134120001) and the Sichuan Province
Foundation of China (No. 09ZA087). |
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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. |
Keywords： |
Reed-Solomon code, Weil bound, Error distance, Rational function,
Trace Reed-Solomon code, Trace map |
Classification： |
30P12, 32C12 |
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