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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Abstract

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
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 14 Jun 2013 15:00
Last Modified: 26 Apr 2022 09:58
URI: https://research.sabanciuniv.edu/id/eprint/21615

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