Simple recursive formulas generating power moments of Kloosterman sums
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Abstract. In this paper, we construct four binary linear codes closely connected with certain exponential sums over the ¯nite ¯eld F_q and F_q - {0, 1}. Here q is a power of two. Then we obtain four recursive formulas for the power moments of Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of the exponential sums obtained earlier.
Abstract
Abstract. In this paper, we construct four binary linear codes closely connected with certain exponential sums over the ¯nite ¯eld F_q and F_q - {0, 1}. Here q is a power of two. Then we obtain four recursive formulas for the power moments of Kloosterman sums in terms of the frequencies of weights in the codes. This is done via Pless power moment identity and by utilizing the explicit expressions of the exponential sums obtained earlier.
참고문헌 (7)
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- D.S.Kim, "Codes associated with O¡(2n; 2r) and power moments of Kloosterman sums", ~
- F. J. MacWilliams, "The Theory of Error Correcting Codes" (1998), North-Holland
- M. Moisio, "The moments of a Kloosterman sum and the weight distribution of a Zetterberg-type binary cyclic code", IEEE Trans. Inform. Theory, 53, pp.843~847 (2007)
- R. Schoof, "Hecke operators and the weight distributions of certain codes", J. Combin. Theory Ser. A, 57, pp.163~186 (1991)