- #1
Icheb
- 42
- 0
I have the following linear transformation
http://img162.imageshack.us/img162/3306/hammingcodeex4.gif
with G being a generating matrix for a hamming code and I have to find a matrix B so that the following:
[tex]\delta \cdot\gamma(\upsilon) = \upsilon[/tex] for all [tex]\upsilon \in Z^4_2[/tex]
is true for the transformation
[tex]\delta := \varphi_B: Z^7_2 \longrightarrow Z^4_2, c \longmapsto Bc[/tex]The way I understand this is that I have to reverse the initial transformation by finding the correct B. I figure it would be sufficient to invert G (since G * G^-1 * v = 1 * v = v and then B = G^-1), but how would that comply with the requirement that the first transformation goes from [tex]Z^4_2[/tex] to [tex]Z^7_2[/tex] and the second one goes the other way round?
If I can't just invert G, how would I go about this then?
http://img162.imageshack.us/img162/3306/hammingcodeex4.gif
with G being a generating matrix for a hamming code and I have to find a matrix B so that the following:
[tex]\delta \cdot\gamma(\upsilon) = \upsilon[/tex] for all [tex]\upsilon \in Z^4_2[/tex]
is true for the transformation
[tex]\delta := \varphi_B: Z^7_2 \longrightarrow Z^4_2, c \longmapsto Bc[/tex]The way I understand this is that I have to reverse the initial transformation by finding the correct B. I figure it would be sufficient to invert G (since G * G^-1 * v = 1 * v = v and then B = G^-1), but how would that comply with the requirement that the first transformation goes from [tex]Z^4_2[/tex] to [tex]Z^7_2[/tex] and the second one goes the other way round?
If I can't just invert G, how would I go about this then?
Last edited by a moderator: