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June 1, 2026Designs Codes and CryptographyOpen Access

There are siblings of χ which are permutations for n even

Björn Kriepke Gohar Kyureghyan

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Key Points

The aim is to explore the properties of bimodal functions in binary vector spaces related to permutations.
Analyzed the vector space generated by functions using binary mathematics.
Defined a family of permutation functions based on component-wise multiplication.
Utilized the cyclic left shift function in calculations.
Described new permutation forms for vectors in binary spaces under specific conditions.
Showed that the generated functions maintain structural coherence within the vector space.

Implication

Demonstrates the properties of permutation functions in binary vector spaces for even dimensions, suggesting new algebraic structures.

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Cite This Study

Kriepke et al. (2026) studied this question.

synapsesocial.com/papers/6a211852d499ed480b170f33 https://doi.org/10.1007/s10623-026-01830-0

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