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Determining Minimized Galois Field Expressions for Ternary Functions by using Special Normal Form

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Original languageEnglish
Pages (from-to)53-71
Number of pages19
JournalJournal of Multiple-Valued Logic and Soft Computing
Issue number1-4
Publication statusPublished - 2015
Publication typeA1 Journal article-refereed


The Special Normal Form (SNF) for Boolean functions is a redundant representation that is useful in determining minimized Exclusive-Or-Sum-Of-Product (ESOP) expressions. Generalized Reed-Muller expressions (GRM) can be viewed as expressions that are close to the ESOPs in the number of products, however, they are easier to determine, which makes them important in practical applications.

Galois field (GF) expressions are a generalization of Reed-Muller expressions to multiple-valued logic functions. This paper extends the notion of SNF for Boolean functions to ternary logic functions. An algorithm to minimize generalized Galois field (GF) expressions for ternary functions by using SNF is presented.

Publication forum classification

Field of science, Statistics Finland