Title :
A multiple-valued Reed-Muller transform for incompletely specified functions
Author :
Zilic, Zeljko ; Vranesic, Zvonko G.
Author_Institution :
Dept. of Electr. & Comput. Eng., Toronto Univ., Ont., Canada
fDate :
8/1/1995 12:00:00 AM
Abstract :
This paper considers the Reed-Muller transform for incompletely specified multiple-valued logic functions, which is obtained as the finite field polynomial representation. A new algorithm for dealing with single-variable functions is presented. It is applicable to finite fields of small sizes (two to four), which is of interest because only these fields are readily implementable with today´s MVL technology. It is shown how such or any similar single-variable algorithm can be used to obtain a fast n-variable Reed-Muller transform based on this transform, a heuristic scheme is derived for dealing with incompletely specified functions. It has better computational properties than other methods and achieves the best results when applied to functions with a large number of unspecified points
Keywords :
Reed-Muller codes; logic design; multivalued logic; computational properties; finite field polynomial representation; heuristic scheme; incompletely specified functions; multiple-valued Reed-Muller transform; multiple-valued logic functions; single-variable algorithm; single-variable functions; Arithmetic; Circuit testing; Cryptography; Field programmable gate arrays; Galois fields; Logic devices; Logic functions; Polynomials; Programmable logic arrays; Programmable logic devices;
Journal_Title :
Computers, IEEE Transactions on
