Homework 1

 

 
 [ 0 0 2 2 0 2 ]
 [ 2 2 0 2 1 2 ]
 [ 1 1 2 0 2 2 ]
 [ 1 1 0 1 2 1 ]
 
 

        Problem 2.
Let V be a binary linear code given by the generator matrix

 
 [ 101011 ]
 G =  [ 011110 ]
 [ 000111 ]

o       a) Find a parity check matrix H of V .

o       b) Construct a maximum likelihood decoding table for V .

o       c) Use H to reduce the maximum likelihood decoding table of b) to an error/syndrome table.

o       d) Demonstrate how your error/syndrome table can be used to decode the received vector r = 111101.

o       e) Use the generator matrix to create a list of all code vectors of V. Then use this list to determine the minimum distance of V.


Last Modified: February 11, 2001