On ternary symmetric bent functions
2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)(2020)
摘要
This work was motivated by the fact that in the binary domain there are exactly 4 symmetric bent functions for every even n. A first study in the ternary domain shows very different properties. There are exactly 36 ternary symmetric bent functions of 2 variables, at least 12 ternary symmetric bent functions of 3 variables and at least 36 ternary symmetric bent functions of 4 variables. Furthermore the concept of strong symmetric bent function is introduced. To generate ternary symmetric 2k-place bent functions the tensor sum of two k-place ternary symmetric and the Maiorana Method were analyzed and combined with a set of spectral invariant operations. For n = 3 ternary symmetric bent functions were studied on a class of bent functions in the Reed-Muller domain, and a special adaptation of the tensor sum method was used, obtaining 18 ternary strong symmetric bent functions.
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关键词
Ternary functions,Symmetric functions,Bent functions
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