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.

• 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?

--Abdull (talk) 17:32, 5 September 2010 (UTC)

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)