American Institute of Mathematical Sciences

Advanced
May  2009, 3(2): 167-178. doi: 10.3934/amc.2009.3.167

Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups

Dae San Kim 1,

1. 

Department of Mathematics, Sogang University, Seoul 121-742, South Korea

Received  December 2008 Revised  April 2009 Published  May 2009

In this paper, we construct two infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroups of the symplectic group $S_p(2n, q)$. Here $q$ is a power of three. Then we obtain infinite families of recursive formulas for the power moments of Kloosterman sums with square arguments and for the even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identities and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of ''Gauss sums'' for the symplectic groups $S_p(2n, q)$.
Keywords: Pless power moment identity, Kloosterman sum, weight distribution., square argument, Ternary linear code, Gauss sum, power moment, symplectic group.
Mathematics Subject Classification: 11T23, 20G40, 94B0.
Citation: Dae San Kim. Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups. Advances in Mathematics of Communications, 2009, 3 (2) : 167-178. doi: 10.3934/amc.2009.3.167
[1]

Thanh Hieu Le, Marc Van Barel. On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 91-102. doi: 10.3934/naco.2016001
[2]

Denis S. Krotov, Patric R. J.  Östergård, Olli Pottonen. Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code. Advances in Mathematics of Communications, 2016, 10 (2) : 393-399. doi: 10.3934/amc.2016013
[3]

Abraão D. C. Nascimento, Leandro C. Rêgo, Raphaela L. B. A. Nascimento. Compound truncated Poisson normal distribution: Mathematical properties and Moment estimation. Inverse Problems & Imaging, 2019, 13 (4) : 787-803. doi: 10.3934/ipi.2019036
[4]

Guanglu Zhou. A quadratically convergent method for minimizing a sum of Euclidean norms with linear constraints. Journal of Industrial & Management Optimization, 2007, 3 (4) : 655-670. doi: 10.3934/jimo.2007.3.655
[5]

Zhen Wang, Xiong Li, Jinzhi Lei. Second moment boundedness of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2963-2991. doi: 10.3934/dcdsb.2014.19.2963
[6]

Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032
[7]

Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007
[8]

Zhiying Qin, Jichen Yang, Soumitro Banerjee, Guirong Jiang. Border-collision bifurcations in a generalized piecewise linear-power map. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 547-567. doi: 10.3934/dcdsb.2011.16.547
[9]

Yuhe Du, Jianwei Ji, Yu Liao, Yichu Liu. Design of energy storage coordination optimization algorithm for distributed power distribution network operation planning. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020206
[10]

Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zero-sum linear-quadratic differential game: Saddle-point equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 1-20. doi: 10.3934/naco.2017001
[11]

Libin Mou, Jiongmin Yong. Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial & Management Optimization, 2006, 2 (1) : 95-117. doi: 10.3934/jimo.2006.2.95
[12]

Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 939-956. doi: 10.3934/dcdsb.2018049
[13]

Zhenning Cai, Yuwei Fan, Ruo Li. On hyperbolicity of 13-moment system. Kinetic & Related Models, 2014, 7 (3) : 415-432. doi: 10.3934/krm.2014.7.415
[14]

Gilberto M. Kremer, Wilson Marques Jr.. Fourteen moment theory for granular gases. Kinetic & Related Models, 2011, 4 (1) : 317-331. doi: 10.3934/krm.2011.4.317
[15]

Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003
[16]

Laura Gardini, Roya Makrooni, Iryna Sushko. Cascades of alternating smooth bifurcations and border collision bifurcations with singularity in a family of discontinuous linear-power maps. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 701-729. doi: 10.3934/dcdsb.2018039
[17]

Xiangxiang Huang, Xianping Guo, Jianping Peng. A probability criterion for zero-sum stochastic games. Journal of Dynamics & Games, 2017, 4 (4) : 369-383. doi: 10.3934/jdg.2017020
[18]

Jean Louis Woukeng. $\sum $-convergence and reiterated homogenization of nonlinear parabolic operators. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1753-1789. doi: 10.3934/cpaa.2010.9.1753
[19]

Marianne Akian, Stéphane Gaubert, Antoine Hochart. Ergodicity conditions for zero-sum games. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3901-3931. doi: 10.3934/dcds.2015.35.3901
[20]

Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks & Heterogeneous Media, 2018, 13 (1) : 155-176. doi: 10.3934/nhm.2018007

2018 Impact Factor: 0.879

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences