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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.

user1362058
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  • The boring answer is probably "it depends on your application". – Arthur Apr 09 '17 at 21:45
  • @Arthur Ya, not what I was hoping to hear. ;) If it helps, we're working with robust quadratic non-repetitive codes. – user1362058 Apr 09 '17 at 22:18
  • From what little I was able to learn of robust quadratic non-repetitive codes in the last few minutes, I don't see any application for negative bits or negative bytes. You might have a better question if you showed the formulas or algorithms in which these "negative bytes" occur. – David K Apr 09 '17 at 22:29
  • @DavidK I hope that edit helps explain it a little better. – user1362058 Apr 09 '17 at 23:03
  • So if $y_1 = 011$ and $e_1 = 010,$ is $y_1+e_1 = 001$ or is $y_1+e_1=101$? The result $101$ is the standard meaning of $+$ for binary integers, but $001$ makes more sense as a transmission with errors. I think people tend to use $\oplus$ for that. I don't know how the "multiplication" is defined unless it's actually intended to be bitwise AND. I haven't found any literature where I see such a thing done, however--everything I've seen is expressed relative to individual bits of a word. – David K Apr 10 '17 at 01:50
  • I think your best bet is to assume your professor and/or textbook is using his/her own theory and notation that nobody else uses, so you have to define everything. Also, use MathJax for your formulas: http://math.stackexchange.com/help/notation – David K Apr 10 '17 at 01:55
  • Thanks @DavidK Multiplication is within the field and addition is XOR. I will definitely use the markup FAQ next time I ask a question. I had a Hangouts with some other classmates a few minutes ago, and we think we came to an agreement on what to do with this problem. Should I answer the question or delete? – user1362058 Apr 10 '17 at 02:58

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