Operations over finite field GF(8)

s35300792001

Suppose that matrix M is

{ {2, -2, 1}, {(-1/2), (1/2), 0}, {(-1/2), (3/2), (-1)} },

then how to calculate the value as follows

{ {2, -2, 1}, {(-1/2), (1/2), 0}, {(-1/2), (3/2), (-1)} } X {(011), (010)}, (100)} = ?

In addition, I read a paper say that let B be the total file size measured in terms of symbols over a finite field Fq of size q.

If there are three symbols A(010), B(110), and C(011), what is the value of 2A+3B+C over the finite field F7?

Thanks.

bnt

That's weird. It's written like a Matrix Multiplication problem, a matrix times a vector, but I don't know the meaning of the vector in this context.

Is it a "mask", where 1 means keep the value, and 0 means not? In that case you'd expand it to
{ { 0, 0, 1 } { 1, 1, 0 } { 1, 0, 0 } }
and do a scalar not vector multiplication, so ending up with

M = { {0, 0, 1} {-1/2, 1/2, 0} {-1/2, 0, 0} }

Either that or the vector has some specialist meaning that's not obvious to me.