Reed–Muller code: Difference between revisions

Revision as of 17:37, 23 May 2022

Revision as of 13:17, 21 November 2022

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+ (0\cdot Z_1 Z_2 + 1\cdot Z_1Z_3 + 0\cdot Z_1Z_4 + 1\cdot Z_2Z_3 + 0\cdot Z_2Z_4+ 1\cdot Z_3Z_4)\\

&=1+Z_1+Z_3+Z_1Z_3+Z_2Z_3+Z_3Z_4

\end{align}</math>Then it evaluates this polynomial at all 16 evaluation points (0101 means <math>X_1=0, X_2=1, X_3=0, X_4=1)</math>:
<math display="block">
p_x(0000)= 1,\;

p_x(0001)= 1,\;

p_x(0010)= 10,\;

p_x(0011)= 1,\;</math>

<math display="block">

p_x(0100)= 1,\;

p_x(0101)= 01,\;

p_x(0110)= 1,\;

p_x(0111)= 0,\;</math>

<math display="block">

p_x(1000)= 0,\;

p_x(1001)= 10,\;

p_x(1010)= 0,\;

p_x(1011)= 1,\;</math>

<math display="block">

p_x(1100)= 0,\;

p_x(1101)= 0,\;

p_x(1110)= 01,\;

p_x(1111)= 0\,.</math>As a result, C(1 1010 010101) = 11111101 10101110 01010001 00000010 holds.

=== Decoder ===