Necessary Conditions for the Existence of Regular p-Ary Bent Functions
- 주제(키워드) p-ary function , p-ary bent function , regular p-ary bent function , MacWilliams duality , Gleason theorem
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000091286
- 본문언어 영어
- Published As http://dx.doi.org/10.1109/TIT.2014.2298867
초록/요약
We find some necessary conditions for the existence of regular p-ary bent functions (from Z(p)(n) to Z(p)), where p is a prime. In more detail, we show that there is no regular p-ary bent function f in n variables with w(M-f) larger than n/2, and for a given nonnegative integer k, there is no regular p-ary bent function f in n variables with w(M-f) = n/2 - k (n + 3/2 - k, respectively) for an even n = N-p,N- (k) (an odd n >= N-p,N- k, respectively), where N-p,N- k is some positive integer, which is explicitly determined and the w(M-f) of a p-ary function f is some value related to the power of each monomial of f. For the proof of our main results, we use some properties of regular p-ary bent functions, such as the MacWilliams duality, which is proved to hold for regular p-ary bent functions in this paper.
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