Spectral Logic and Its Applications for the Design of Digital Devices

ACRONYMS

G	Finite group of order g = |G| (usually direct product of m groups Gi of orders gi =|Gi|)
C2	Cyclic group of order 2
.	Direct product of m cyclic groups C2, also called the finite dyadic group of order 2m
Cp	Cyclic group of order p
.	Direct product of m copies of Cp
χw	Character of G with the index w
uw	Unitary irreducible representation of G with the index w
P	Field
C	Field of complex numbers
R	Field of real numbers
Z	Set of integers
GF(pm)	Field of p-ary m-dimensional vectors
z	Variable in P
z = (z0, …, zm−1)	Componentwise representation of z on .
||z||	Hamming norm of z (number of non-zero components in the componentwise representation of z)
f(z)	Function over P in the variable z ∈ G
f (z0, …,zm−1)	Function over P of m variables zi ∈ Gi
f = (f(0), …,f(k−1))	System of k functions also called a k-output function f
f (z)	Integer function corresponding to a k-output function f .
Φ(z)	Piecewise constant function corresponding toa k-output function f
Ww(z)	Discrete Walsh function of the index w and the argument z
W(m)	(2m × 2m) Walsh ...