Boolean functions with MacWilliams duality
- 주제(키워드) Bent function , Self-dual bent function , Formally self-dual function , MacWilliams-dual function , Formally self-dual pair , MacWilliams duality
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 SPRINGER
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000091287
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/s10623-012-9762-7
초록/요약
We introduce a new class of Boolean functions for which the MacWilliams duality holds, called MacWilliams-dual functions, by considering a dual notion on Boolean functions. By using the MacWilliams duality, we prove the Gleason-type theorem on MacWilliams-dual functions. We show that a collection of MacWilliams-dual functions contains all the bent functions and all formally self-dual functions. We also obtain the Pless power moments for MacWilliams-dual functions. Furthermore, as an application, we prove the nonexistence of bent functions in 2n variables with minimum degree n-k for any nonnegative integer k and n a parts per thousand yen N with some positive integer N under a certain condition.
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