a) List all the codewords in C. b) Find a parity check matrix for C.

6.) Find the rank of the matrix A 2031 0211 32 11 5453

Given the binary linear code C = {00000000, 01101111, 11011000, 11111101, 10010010, 00100101, 01001010, 10110111}. (a) Find two distinct generator matrices for C. (b) What is the dimension of C? (c) Show that the two matrices in (a) correspond to two distinct ways of encoding messages. (d) What are the three parameters n, k, and d for C?

Encode the message "THE EAGLE HAS LANDED" using the 5x5 encoding matrix C given below. Form a matrix with 5 rows and as many columns as necessary to accommodate the message. The letters A-Z are assigned to the numbers 1-26 and 0 is assigned the blank or space character "". 01103 10101 C 2 1 1 1 1 00102 11 12 1 Represent the message as an array of numbers where columns are filled from top to bottom and where entries that do not correspond to message characters are set to 0. 0 (Type an integer or simplified fraction for each matrix element.)