Homework 2

Due: Thursday, September 25, 1997

Problem 1.
Over GF(3), put the following matrix into echelon canonical form
[ 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 ]

a) Find a parity check matrix H of V .

b) Construct a maximum likelihood decoding table for V .

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

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

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: September 25, 1997