On the weight distribution of the duals of irreducible cyclic codes, cyclic codes with two zeros and hyper-Kloosterman codes
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چکیده
This paper considers the weight distributions of binary cyclic codes with one or two zeros and hyper-Kloosterman codes. The results on value distributions of certain monomial exponential sums and connections between exponential sums and Kloosterman sums are applied together with the Pless power moment identity in these conciderations. Explicit formulae for the number of low-weight codewords are given as well as the entire weight distribution for some classes of codes. We show that the minimum distance of the cyclic codes with one zero, ie. the duals of irreducible cyclic codes, in so-called index 2 case is three except for two codes. Finally, computational results are presented showing the number of small weight codewords for several codes and the entire weight distribution for some codes.
منابع مشابه
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تاریخ انتشار 2007