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Infinite families of recursive formulas generating power moments of Kloosterman sums: O − (2 n ,2 r ) case

In this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO − (2 n , 2 r ). And we obtain four infinite families of recursive formulas for the power moments of Klooste... Full description

Journal Title: Mathematica Slovaca 2013, Vol.63(4), pp.733-758
Main Author: Kim, Dae
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0139-9918 ; E-ISSN: 1337-2211 ; DOI: 10.2478/s12175-013-0132-3
Link: http://dx.doi.org/10.2478/s12175-013-0132-3
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recordid: springer_jour10.2478/s12175-013-0132-3
title: Infinite families of recursive formulas generating power moments of Kloosterman sums: O − (2 n ,2 r ) case
format: Article
creator:
  • Kim, Dae
subjects:
  • Kloosterman sum
  • 2-dimensional Kloosterman sum
  • orthogonal group
  • special orthogonal group
  • double cosets
  • maximal parabolic subgroup
  • Pless power moment identity
  • weight distribution
ispartof: Mathematica Slovaca, 2013, Vol.63(4), pp.733-758
description: In this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO − (2 n , 2 r ). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional 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 exponential sums over those double cosets related to the evaluations of “Gauss sums” for the orthogonal groups O − (2 n , 2 r ).
language: eng
source:
identifier: ISSN: 0139-9918 ; E-ISSN: 1337-2211 ; DOI: 10.2478/s12175-013-0132-3
fulltext: fulltext
issn:
  • 1337-2211
  • 13372211
  • 0139-9918
  • 01399918
url: Link


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subjectKloosterman sum ; 2-dimensional Kloosterman sum ; orthogonal group ; special orthogonal group ; double cosets ; maximal parabolic subgroup ; Pless power moment identity ; weight distribution
descriptionIn this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO − (2 n , 2 r ). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional 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 exponential sums over those double cosets related to the evaluations of “Gauss sums” for the orthogonal groups O − (2 n , 2 r ).
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titleInfinite families of recursive formulas generating power moments of Kloosterman sums: O − (2 n ,2 r ) case
descriptionIn this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO − (2 n , 2 r ). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional 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 exponential sums over those double cosets related to the evaluations of “Gauss sums” for the orthogonal groups O − (2 n , 2 r ).
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12-dimensional Kloosterman sum
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abstractIn this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to a certain maximal parabolic subgroup of the special orthogonal group SO − (2 n , 2 r ). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional 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 exponential sums over those double cosets related to the evaluations of “Gauss sums” for the orthogonal groups O − (2 n , 2 r ).
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