Talk:Balanced boolean function

Wrong examples?
Currently, the following examples are given
 * An example of a balanced boolean function is the function that assigns a 1 to every even number and 0 to all odd numbers (likewise the other way around). The same applies for functions assigning 1 to all positive numbers and 0 otherwise.

--Abdull (talk) 17:32, 5 September 2010 (UTC)
 * Regarding the first example: even numbers and odd numbers are of type integer, not of type boolean - therefore the first example is not an example of an boolean function.
 * Regarding the second example: 0 is usually understood as being neither positive nor negative. Therefore there will be one more element in the set that is assigned 0 compared to the set that is assigned 1. Is it correct to still speak of this function being balanced?

This page was copied from the abstract of the article cited!

It needs to be deleted or re-written. — Preceding unsigned comment added by 131.122.6.28 (talk) 12:21, 20 March 2012 (UTC)

In my opinion, this article is very weak. I have never edited wikipedia but I have two suggestions. These should make the article more useful for researchers.

1. Mention some elementary properties of balanced boolean functions.

Example 1: a balanced boolean function of dimension D+1 can be created by concatenating any dimension D boolean function with its complement. Example 2: balanced boolean functions have the unique property that their complement is also balanced. Example 3: The randomization lemma (See the famous coding theory book by Sloane and MacWilliams)

2. Mention the Cusick-Cheon conjecture.

The Cusick-Cheon conjecture deals with a fundamental characterization of balanced boolean functions in terms of the degree of their algebraic normal form representation.

It is very likely that the Cusick-Cheon conjecture is true because it is backed by good numerical evidence although it has only been proven in special cases. — Preceding unsigned comment added by 24.179.214.114 (talk) 21:54, 31 May 2019 (UTC)