The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
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Reed-Muller like canonic (m-RMC) expansions for multivalued functions have been proposed earlier. For a n-variable m-valued function there are mnexpansions. This paper is related to the problem of finding minimal m-RMC expansions. Each of the expansions are determined by mn unknown coefficients in them. Thus there are altogether m2n coefficients. It is shown that only m(m+1)/n2 coefficients are distinct and hence by computing these coefficients one can determine all the mn expansions. Further, it is shown that the number of distinct coefficients for symmetric functions is reduced to [equation].