Title page for etd-0727111-194912


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URN etd-0727111-194912
Author Tzu-Wei Jen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2010
Semester 2
Degree Master
Type of Document
Language English
Title Generalized minimal polynomial over finite field and its application in coding theory
Date of Defense 2011-06-20
Page Count 37
Keyword
  • generalized minimal polynomial
  • generalized conjugate element
  • unknown syndrome
  • quadratic residue code
  • Lagrange interpolation formula
  • Abstract      In 2010, Prof. Chang and Prof. Lee applied Lagrange interpolation formula to decode a class of binary cyclic codes, but they did not provide an effective way to calculate the Lagrange interpolation formula. In this thesis, we use the least common multiple of polynomials to compute it effectively.
    Let E be an extension field of degree m over F = F_p and β be a primitive nth root of unity in E. For a nonzero element r in E, the minimal polynomial of r over F is denoted by m_r(x). Then, let Min (r, F) denote the least common multiple of m_rβ^i(x) for i = 0, 1,..., n-1 and be called the generalized minimal polynomial of over F. For any binary quadratic residue code mentioned in this thesis, the set of all its correctable error patterns can be partitioned into root sets of some generalized minimal polynomials over F. Based on this idea, we can develop an effective method to calculate the Lagrange interpolation formula.
    Advisory Committee
  • D. J. Guan - chair
  • Tzon-Tzer Lu - co-chair
  • C. D. Lee - co-chair
  • Yaotsu Chang - advisor
  • Tsai-Lien Wong - advisor
  • Files
  • etd-0727111-194912.pdf
  • indicate not accessible
    Date of Submission 2011-07-27

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