Wizz kids needed

[manni]

i have a tricky question in which i need help with the terminology

here it is:

given a matrix A ∈ B^(m x n) and a vector b ∈ B^m, define (hashing) h,H,b: B^n → B^m by h,A,b(u) = Au + b, where arithmetic in B is modulo 2, show that the family

H,n,m = {h,A,b: A ∈ B^(m x n), b ∈ B^m } is a strongly 2-universal family of hash functions?

- what does it mean for arithmetic in B to be modulo 2?
- is the hash function taking values from Bn to Bm?
- how to approach this any ideas?

[Moschops]

what does it mean for arithmetic in B to be modulo 2?

It means the sequence of numbers, adding one each time, goes like this:

0,1,0,1,0,1,0,1 .....

1+1 = 0 in modulo two.