POWER MOMENTS OF KLOOSTERMAN SUMS AND CODES ASSOCIATED WITH SYMPLECTIC GROUPS
- 발행기관 서강대학교 수학과 대학원
- 지도교수 김 대 산
- 발행년도 2009
- 학위수여년월 2009. 8
- 학위명 박사
- 학과 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000045401
- 본문언어 영어
- 저작권 서강대학교의 논문은 저작권에 의해 보호받습니다
초록/요약
In this thesis, we obtain several recursive formulas generating power moments of Kloosterman sums over finite fields of characteristic two and three. First, we construct binary linear codes associated with the symplectic groups Sp(4,q). Here q is a power of two. Then we derive recursive formulas for even power moments of Kloosterman sums or equivalently for power moments of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes. Next, we treat the case of q=3^r. We construct two ternary linear codes associated with the symplectic groups Sp(2,q)and Sp(4,q). Then we obtain 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. These are done via Pless power moment identity and by utilizing the explicit expressions of "Gauss sums" for the symplectic groups Sp(2n,q).
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