Majority Logic Decoding
Instructions

    Procedure:
  • Step 1: Select the bits of the check set by clicking on the bits. After selecting the bits, click on the "Check" button to check if the selected bits are correct.
  • Step 2: If the selected bits are correct, the "Next" button will appear and observation section will say it is correct. If the selected bits are not correct, the observation section will say it is wrong and you can try again.
  • Step 3: After clicking on the "Next" button, you can select the next check set. Again, click on the "Check" button to check if the selected bits are correct.
  • Step 4: After selecting all the sub-codewords for the monomial, the observation section will say all check sets are completed and the "Next" button will be hidden. Press "New Question" to try a new example.


Consider a codeword,

  from the     code.

Consider the coordinates of the codeword being ordered in lexicographic order that is \((X_1, X_2, X_3, X_4)\) taking values from \((0,0,0,0)\), \((0,0,0,1)\) to \((1,1,1,1)\). Then, for the monomial , select the check sums:

Observations