TERNARY FUNCTIONS WITH BENT REED-MULLER-FOURIER SPECTRA

被引：0

作者：

Moraga, Claudio ^{[1
,2
]}

Stankovic, Radomir ^{[3
,4
]}

Stankovic, Milena ^{[5
]}

机构：

[1] Tech Univ Dortmund, D-44221 Dortmund, Germany

[2] Univ Tecn Federico Santa Maria, Valparaiso, Chile

[3] Fac Elect Engn, Dept Comp Sci, Niaa 18000, Serbia

[4] Math Inst SASA, Belgrade 11000, Serbia

[5] Univ Nis, Fac Elect Engn, Nish 18000, Serbia

来源：

JOURNAL OF APPLIED LOGICS-IFCOLOG JOURNAL OF LOGICS AND THEIR APPLICATIONS | 2022年 / 9卷 / 03期

关键词：

RMF transform; bent functions; restricted tensor sum;

D O I：

暂无

中图分类号：

B81 [逻辑学（论理学）];

学科分类号：

010104 ; 010105 ;

摘要：

Ternary functions which have a bent Reed-Muller-Fourier (RMF) spectrum are introduced. Necessary conditions for a function to have this property are established. A classification of ternary 2-place functions having a bent RMF spectrum in 6 classes is given and it is shown that these classes are related by spectral invariance operations. Moreover, a compact database of those ternary functions with bent RMF spectra is provided. Ternary bent functions having the same value vector as their respective RMF bent spectra are known as fixed points. The paper generalizes this concept to rotational fixed points when the value vector of a function equals its spectra shifted by a constant. Finally, a method is introduced to generate n-place ternary functions with bent RMF spectrum when n > 2.

引用

页码：737 / 756

页数：20

共 50 条

[41] Fourier transforms and bent functions on finite groups
Fan, Yun
Xu, Bangteng
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (09) : 2091 - 2113
[42] Remarks on Similarities Among Ternary Bent Functions
Stankovic, Radomir S.
Stankovic, Milena
Astola, Jaakko T.
Moraga, Claudio
[J]. 2019 IEEE 49TH INTERNATIONAL SYMPOSIUM ON MULTIPLE-VALUED LOGIC (ISMVL), 2019, : 79 - 84
[43] Relationship between Haar Wavelet and Reed-Muller spectra
Falkowski, BJ
[J]. PROCEEDINGS OF THE 2003 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL IV: DIGITAL SIGNAL PROCESSING-COMPUTER AIDED NETWORK DESIGN-ADVANCED TECHNOLOGY, 2003, : 548 - 551
[44] Ternary fixed polarity linear Kronecker transforms and their comparison with ternary Reed-Muller transform
Fu, C
Falkowski, BJ
[J]. JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS, 2005, 14 (04) : 721 - 733
[45] On Learning Boolean Functions and Punctured Reed-Muller-Codes
Schober, Steffen
Bossert, Martin
[J]. 2009 IEEE INFORMATION THEORY WORKSHOP (ITW 2009), 2009, : 465 - 469
[46] Decomposition of logic functions in Reed-Muller spectral domain
Hrynkiewicz, Edward
Kolodzinski, Stefan
[J]. PROCEEDINGS OF THE 2007 IEEE WORKSHOP ON DESIGN AND DIAGNOSTICS OF ELECTRONIC CIRCUITS AND SYSTEMS, 2007, : 219 - +
[47] Simplified Reed-Muller expressions for residue threshold functions
Quintana, JM
Avedillo, MJ
Huertas, JL
[J]. 2002 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL IV, PROCEEDINGS, 2002, : 599 - 602
[48] Hybrid Reed-Muller Haar Representations of Logic Functions
Minasyan, Susanna
Stankovic, Radomir
Egiazarian, Karen
Astola, Jaakko
[J]. JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING, 2009, 15 (04) : 341 - 359
[49] Simplified Reed-Muller expressions for residue threshold functions
Quintana, JM
Avedillo, MJ
Huertas, JL
[J]. CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2004, 23 (01) : 45 - 56
[50] REED-MULLER LIKE CANONIC FORMS FOR MULTIVALUED FUNCTIONS
PRADHAN, DK
PATEL, AM
[J]. IEEE TRANSACTIONS ON COMPUTERS, 1975, C 24 (02) : 206 - 210

← 1 2 3 4 5 →