On the minimum distance of cyclic codes

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Işık, Leyla (2011) On the minimum distance of cyclic codes. [Thesis]

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Estimation of the minimum distance of cyclic codes is a classical problem in coding theory. Using the trace representation of cyclic codes and Hilbert's Theorem 90, Wolfmann found a general estimate for the minimum distance of cyclic codes in terms of the number of rational points on certain Artin-Schreier curves. In this thesis, we try to understand if Wolfmann's bound can be improved by modifying equations of the Artin-Schreier curves by the use of monomial and some nonmonomial permutation polynomials. Our experiments show that an improvement is possible in some cases.

Item Type:Thesis
Uncontrolled Keywords:Finite fields. -- Cyclic codes. -- Trace representations. -- Permutation polynomials. -- Sonlu cisimler. -- Devirsel kodlar.-- İz gösterimleri. -- Permütasyon polinomları.
Subjects:Q Science > QA Mathematics
ID Code:21615
Deposited By:IC-Cataloging
Deposited On:14 Jun 2013 15:00
Last Modified:25 Mar 2019 17:05

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