Reed–Muller expansion
Reed–Muller expansion is a way to express a number as the sum of different sets of numbers. We can think of it like adding up different sets of Lego pieces to make a big tower.
We start by writing down a bunch of numbers that are either 0 or 1. 0 means "no Lego" while 1 means "one Lego". Then, we take the sets of numbers that contain ones (1s) and write them as exponents of two. For example, if the numbers are 10001, then we are adding two sets of Lego pieces, two and sixteen. This is because "1" means "one", and "0" means "no". 2^3 (eight) plus 2^0 (one) equals nine.
In the end, we have expressed a bigger number (the sum of our Legos) as the sum of different sets of smaller numbers that are either 0 or 1. This is called the Reed–Muller expansion.
We start by writing down a bunch of numbers that are either 0 or 1. 0 means "no Lego" while 1 means "one Lego". Then, we take the sets of numbers that contain ones (1s) and write them as exponents of two. For example, if the numbers are 10001, then we are adding two sets of Lego pieces, two and sixteen. This is because "1" means "one", and "0" means "no". 2^3 (eight) plus 2^0 (one) equals nine.
In the end, we have expressed a bigger number (the sum of our Legos) as the sum of different sets of smaller numbers that are either 0 or 1. This is called the Reed–Muller expansion.