The divisibility modulo 24 of Kloosterman sums on \(\text{GF}(2^m)\), \(m\) odd
This paper continues previous work by the authors. Here they exploit the connection between binary primitive extended BCH codes of length \(2^m\) (\(m\) odd) with minimal distance 8 and Kloosterman sums over finite fields of order \(2^m\). Some properties on the divisibility of the inverse-cubic sums have been derived. In Theorem 2, the authors state the key congruences which allow computation of the divisibility of Kloosterman sums modulo 24. The results of Theorem 3 provide six different cases which depend each on the form of \(m\). In section 5, the connection between Kloosterman sums and the \([2^m+ 1,2m]\) irreducible code have been recalled and the consequences of the authors' results on the weight distribution of this code have been explained. Finally, the spectrum of Kloosterman sums has been studied.
scientific article; zbMATH DE number 5129735
scientific article