Canonical form it is well known that every linear code can be put in canonical form we discuss the exact meaning of this term and show how the reed- muller codes can be put in this form consider any (n, k) code, that is, we have a subspace a of dimension k in the n-dimensional space v and a fixed basis ~, , v~ of v.
Canonical restricted mixed-polarity exclusive-or sums of products and the efficient algorithm for their minimisation l csanky ma perkowski i schafer indexing terms ’ boolean algebra, logic, reed-muller,form minimisation abstract: the concept of canonical restricted mixed polarity (crmp) exclusive-or sum of pro-. Other canonical forms include the complete sum of prime implicants or blake canonical form (and its dual), and the algebraic normal form (also called zhegalkin or reed–muller) minterms are called products because they are the logical and of a set of variables, and maxterms are called sums because they are the logical or of a set of variables.
The expression which will be obtained after simplification will be called a positive or true polarity reed-muller expression because the variables appear in the true form only now a 3-variable function f ( a , b , c ) which is written in canonical sop form can be transformed into positive xor-and form using the following procedure. Keywords: logic synthesis tabular technique map technique reed–muller canonical or coincidence 1 introduction any n-variable boolean function can be represented in either canonical sum-of-products (csop) or canonical product-of-sums (cpos) form csop expansions are based on the and/or forms and.
On the calculation of generalized reed-muller canonical expansions from disjoint cube representation of boolean functions bogdan j falkowski marek a perkowski department of electrical engineering.