What is the meaning for a vector mod a matrix in a lattice? I'm reading about the lattice recently.In the paper, it gives a method of a vector mod a matrix:

⃗c mod B as ⃗c−⌊⃗c×B^(−1)⌉×B = [⃗c×B^(−1)]×B.

I know that a integer A mod the other integer B is A+-kB, to make A in the defined field B.

Can anyone tell me what is the meaning of a vector mod a matrix and the mid term ⌊⃗c×B^(−1)⌉ means?:(

Tks.
A vector u mod a matrix B is ​ u ± Bv . ​ ​ ​ We are modding an element of the vector space's

additive group by the range of the restriction of B to vectors whose entries are all integers.

The parallelepiped given by B's columns is a fundamental domain for the range of that restriction.

⌊⃗c×B−1⌉ is probably rounding each entry of c×B−1 to the nearest integer. ​ If that's correct, then they are using the lattice representation, which corresponds to using [the translation of the parallelepiped I mentioned which sends its center to the origin] as the fundamental domain.