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]

Claude Carlet, Stjepan Picek. On the exponents of APN power functions and Sidon sets, sum-free sets, and Dickson polynomials. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021064
[2]

Abraão D. C. Nascimento, Leandro C. Rêgo, Raphaela L. B. A. Nascimento. Compound truncated Poisson normal distribution: Mathematical properties and Moment estimation. Inverse Problems and Imaging, 2019, 13 (4) : 787-803. doi: 10.3934/ipi.2019036
[3]

Thanh Hieu Le, Marc Van Barel. On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials. Numerical Algebra, Control and Optimization, 2016, 6 (2) : 91-102. doi: 10.3934/naco.2016001
[4]

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
[5]

Toshiharu Sawashima, Tatsuya Maruta. Nonexistence of some ternary linear codes with minimum weight -2 modulo 9. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021052
[6]

Zhen Wang, Xiong Li, Jinzhi Lei. Second moment boundedness of linear stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2963-2991. doi: 10.3934/dcdsb.2014.19.2963
[7]

Guanglu Zhou. A quadratically convergent method for minimizing a sum of Euclidean norms with linear constraints. Journal of Industrial and Management Optimization, 2007, 3 (4) : 655-670. doi: 10.3934/jimo.2007.3.655
[8]

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
[9]

Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007
[10]

Rumi Melih Pelen. Three weight ternary linear codes from non-weakly regular bent functions. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022020
[11]

Zhiying Qin, Jichen Yang, Soumitro Banerjee, Guirong Jiang. Border-collision bifurcations in a generalized piecewise linear-power map. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 547-567. doi: 10.3934/dcdsb.2011.16.547
[12]

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

Gilberto M. Kremer, Wilson Marques Jr.. Fourteen moment theory for granular gases. Kinetic and Related Models, 2011, 4 (1) : 317-331. doi: 10.3934/krm.2011.4.317
[14]

Mohammed Al-Azba, Zhaohui Cen, Yves Remond, Said Ahzi. Air-Conditioner Group Power Control Optimization for PV integrated Micro-grid Peak-shaving. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3165-3181. doi: 10.3934/jimo.2020112
[15]

Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zero-sum linear-quadratic differential game: Saddle-point equilibrium sequence. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 1-20. doi: 10.3934/naco.2017001
[16]

Libin Mou, Jiongmin Yong. Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method. Journal of Industrial and Management Optimization, 2006, 2 (1) : 95-117. doi: 10.3934/jimo.2006.2.95
[17]

Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 939-956. doi: 10.3934/dcdsb.2018049
[18]

René Carmona, Kenza Hamidouche, Mathieu Laurière, Zongjun Tan. Linear-quadratic zero-sum mean-field type games: Optimality conditions and policy optimization. Journal of Dynamics and Games, 2021, 8 (4) : 403-443. doi: 10.3934/jdg.2021023
[19]

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
[20]

Swann Marx, Tillmann Weisser, Didier Henrion, Jean Bernard Lasserre. A moment approach for entropy solutions to nonlinear hyperbolic PDEs. Mathematical Control and Related Fields, 2020, 10 (1) : 113-140. doi: 10.3934/mcrf.2019032

2020 Impact Factor: 0.935

Tools

Metrics

  • PDF downloads (80)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy