DISTRIBUTION OF THE WEIGHTS OF THE KLOOSTERMAN CODE
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 3
Abstract
Tran The Vinh. Distribution of the weights of the Kloosterman code. Studied 𝑝-ary Kloosterman codes of length 𝑝2 − 1 in alphabet F𝑞 which are the cyclic codes of the dual Melas code of length 𝑝2 − 1. We obtain the weight distribution of the Melas codes in terms of one-dimensional Kloosterman sums over the ring of Gaussian integers. Derived the non-trivial bound of sum of the Kloosterman sums 𝑘(1, 𝛼𝑧2; 𝑝), 𝛼 ∈ 𝐺𝑝, when 𝛼 runs the system of reduced residues modulo 𝑝 in Z.
Authors and Affiliations
Tran The Vinh
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