understanding LWE public key algorithm I'm trying to understand this LWE public key system



say I use matrix A = [[44, 73, 20, 54],[92, 19, 78, 22],[31, 34, 94, 29],[82, 32, 70, 68]]

q = 97

bit = 1

and secret key s: [56, 90, 0, 46]

and secret error vector e:[1, 0, -1, 0]

then B = As+e mod q is [73 17 18 27]

Bob's secret is [1, 0, 1, 1]

Bobby computes u = A*x mod q and get [21, 95,57, 26]

and v = Bx + bit(q/2) mod q and get 69

Alice decrypts:

v-s*u = 69 - 58 = 11

11 is quiet far from q/2 = 48

what am i doing wrong?
The message bit should be just that, a single bit, and $v$ should be a single integer modulo $q$. I am not sure how you’re getting $v$ to be a vector. Note that $b^t x$ is an inner product (mod $q$), so it is also a single integer mod $q$.