Journal of the Korean Mathematical Society (대한수학회지)
- Volume 48 Issue 2
- /
- Pages.267-288
- /
- 2011
- /
- 0304-9914(pISSN)
- /
- 2234-3008(eISSN)
DOI QR Code
INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O-(2n, q)
- Kim, Dae-San (DEPARTMENT OF MATHEMATICS SOGANG UNIVERSITY)
- Received : 2009.09.11
- Published : 2011.03.01
Abstract
In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group
File
Acknowledgement
Supported by : National Foundation of Kor
References
- R. J. Evans, Seventh power moments of Kloosterman sums, Israel J. Math. 175 (2010), 349-362. https://doi.org/10.1007/s11856-010-0014-0
- G. van der Geer, R. Schoof, and M. van der Vlugt, Weight formulas for ternary Melas codes, Math. Comp. 58 (1992), no. 198, 781-792. https://doi.org/10.1090/S0025-5718-1992-1122080-4
- K. Hulek, J. Spandaw, B. van Geemen, and D. van Straten, The modularity of the Barth-Nieto quintic and its relatives, Adv. Geom. 1 (2001), no. 3, 263-289. https://doi.org/10.1515/advg.2001.017
-
D. S. Kim, Gauss sums for
$O^{-}$ (2n; q), Acta Arith. 80 (1997), no. 4, 343-365. -
D. S. Kim,Exponential sums for
$O^{-}$ (2n; q) and their applications, Acta Arith. 97 (2001), no. 1, 67-86. https://doi.org/10.4064/aa97-1-4 - D. S. Kim, Gauss sums for symplectic groups over a finite field, Monatsh. Math. 126 (1998), no. 1, 55-71. https://doi.org/10.1007/BF01312455
- D. S. Kim, Exponential sums for symplectic groups and their applications, Acta Arith. 88 (1999), no. 2, 155-171. https://doi.org/10.4064/aa-88-2-155-171
- D. S. Kim, Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups, Adv. Math. Commun. 3 (2009), no. 2, 167-178. https://doi.org/10.3934/amc.2009.3.167
-
D. S. Kim, Ternary codes associated with
$O^{-}$ (2n; q) and power moments of Kloosterman sums with square arguments, submitted. - D. S. Kim, Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums, submitted.
- D. S. Kim and J. H. Kim, Ternary codes associated with symplectic groups and power moments of Kloosterman sums with square arguments, submitted.
-
H. D. Kloosterman, On the representation of numbers in the form
$ax^{2}+by^{2}+cz^{2}+dt^{2}$ , Acta Math. 49 (1927), no. 3-4, 407-464. https://doi.org/10.1007/BF02564120 - R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia Math. Appl. 20, Cambridge University Pless, Cambridge, 1987.
- R. Livne, Motivic orthogonal two-dimensional representations of Gal(Q/Q), Israel J. Math. 92 (1995), no. 1-3, 149-156. https://doi.org/10.1007/BF02762074
- F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1998.
- M. Moisio, On the moments of Kloosterman sums and fibre products of Kloosterman curves, Finite Fields Appl. 14 (2008), no. 2, 515-531. https://doi.org/10.1016/j.ffa.2007.06.001
- C. Peters, J. Top, and M. van der Vlugt, The Hasse zeta function of a K3 surface related to the number of words of weight 5 in the Melas codes, J. Reine Angew. Math. 432 (1992), 151-176.
- H. Salie, Uber die Kloostermanschen Summen S(u; v; q), Math. Z. 34 (1932), no. 1, 91-109. https://doi.org/10.1007/BF01180579
- I. E. Shpalinski, Exponential Sums in Coding Theory and Cryptography, Lecture Notes of Tutorial Lectures given at the Institute of Mathematics of the NUS, Singapore, July 23-26, 2001.