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

Zhiyu Zhao, Fei Wu, Shengsheng Yu, Jingli Zhou

Research output: Contribution to journalArticle

4 Citations (Scopus)

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(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.

Original languageEnglish (US)
Pages (from-to)70-72
Number of pages3
JournalHuazhong Keji Daxue Xuebao (Ziran Kexue Ban)/Journal of Huazhong University of Science and Technology (Natural Science Edition)
Volume33
Issue number2
StatePublished - Feb 2005

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Table lookup
Polynomials
Decoding

Keywords

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

ASJC Scopus subject areas

  • Management of Technology and Innovation

Cite this

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title = "Fast lookup table algorithm for finding roots of quadric or cubic polynomials in the GF(2m)",
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(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.",
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AU - Zhao, Zhiyu

AU - Wu, Fei

AU - Yu, Shengsheng

AU - Zhou, Jingli

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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.

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