On the minimum distance of cyclic codes
Işık, Leyla (2011) On the minimum distance of cyclic codes. [Thesis]
Official URL: http://192.168.1.20/record=b1307448 (Table of Contents)
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.
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