### 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) |
---|---|

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 2005 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Management of Technology and Innovation

### Cite this

**Fast lookup table algorithm for finding roots of quadric or cubic polynomials in the GF(2 ^{m}).** / Zhao, Zhiyu; Wu, Fei; Yu, Shengsheng; Zhou, Jingli.

Research output: Contribution to journal › Article

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*Huazhong Keji Daxue Xuebao (Ziran Kexue Ban)/Journal of Huazhong University of Science and Technology (Natural Science Edition)*, vol. 33, no. 2, pp. 70-72.

}

TY - JOUR

T1 - Fast lookup table algorithm for finding roots of quadric or cubic polynomials in the GF(2m)

AU - Zhao, Zhiyu

AU - Wu, Fei

AU - Yu, Shengsheng

AU - Zhou, Jingli

PY - 2005/2

Y1 - 2005/2

N2 - 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(2m). When m is increasing, the number of searches or the volume of the lookup table rapidly scale up by 2m, 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 x2 + ax + b or a cubic one, x3 + 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.

AB - 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(2m). When m is increasing, the number of searches or the volume of the lookup table rapidly scale up by 2m, 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 x2 + ax + b or a cubic one, x3 + 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.

KW - Chien search

KW - Error correcting code

KW - Error locator polynomial

KW - Lookup table

UR - http://www.scopus.com/inward/record.url?scp=16644377224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=16644377224&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:16644377224

VL - 33

SP - 70

EP - 72

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

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

SN - 1671-4512

IS - 2

ER -