Artin–Schreier curves and weights of two-dimensional cyclic codes |
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Authors: | Cem Güneri |
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Institution: | Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey |
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Abstract: | Let
be the finite field with q elements of characteristic p,
be the extension of degree m>1 and f(x) be a polynomial over
. The maximum number of affine
-rational points that a curve of the form yq−y=f(x) can have is qm+1. We determine a necessary and sufficient condition for such a curve to achieve this maximum number. Then we study the weights of two-dimensional (2-D) cyclic codes. For this, we give a trace representation of the codes starting with the zeros of the dual 2-D cyclic code. This leads to a relation between the weights of codewords and a family of Artin–Schreier curves. We give a lower bound on the minimum distance for a large class of 2-D cyclic codes. Then we look at some special classes that are not covered by our main result and obtain similar minimum distance bounds. |
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Keywords: | Artin– Schreier curve 2-D cyclic code Trace code |
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