### Abstract

In decoding of BCH or RS, Chien search or a lookup table are usually used for finding roots of an error locator polynomial σ(x) in the GF(2^{m}). When m is increasing, the number of searches or the volume of the lookup table rapidly scale up by 2^{m}, and therefore greatly increase the time and space expenses needed by the process of roots finding. These two methods are not economical especially when m is large and the degree of σ(x) is very small, for example, 2 or 3. This paper presented a fast lookup table based an algorithm for finding roots of a quadric error locator polynomial x^{2} + ax + b or a cubic one, x^{3} + ax + bx + c. The new algorithm simplifies the original lookup table of the former polynomials, and the theoretical analysis shows that it needs much less storage volume than the direct lookup table based an algorithm and at the same time is much faster than the traditional Chien search method.

Original language | English (US) |
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Pages (from-to) | 70-72 |

Number of pages | 3 |

Journal | Huazhong Keji Daxue Xuebao (Ziran Kexue Ban)/Journal of Huazhong University of Science and Technology (Natural Science Edition) |

Volume | 33 |

Issue number | 2 |

State | Published - Feb 1 2005 |

### Keywords

- Chien search
- Error correcting code
- Error locator polynomial
- Lookup table

### ASJC Scopus subject areas

- Computer Science(all)