I am working on codes in a class and I need to work with negative bits and "byte" values. I get that a negative 1 is still a 1. Does that still apply when you make a "byte" or "word" of bits?
I could see the argument going either way:
Treat the string of bits each as bits individually or the entire "byte" as a q-ary value.
-011 = 011?
or
-011 = -3 (mod(8)) = 101?
Edit:
To better expand as requested. I made the assumption it was a straight forward question, sorry about that.
I have an error: (010 100 011 010 000) corresponding to inputs (y_1, y_2, y_3, y_4, w)
I want to look for codewords that are masked by this error using the following equation:
(y_1 + e_1)(y_2 + e_2) + (y_3 + e_3)(y_4 + e_4) = y_1*y_2 + y_3*y_4 + e_w
In finding a masked codeword I input an error into the equation and solve for one of the input variables. To do this I need to move some of the e_x variables to the opposite side of the equation and I was having an issue on how I should be treating the error values, binary or q-ary.