Homework 5

Due: Monday, March 9, 1998

Problem 1.  Consider  GF(33)  defined by the primitive polynomial  p(x) = x3 + 2x + 1, and let  ksi = x mod p(x).  Find the minimum polynomial  m5(x)  of  ksi5.   You may assume the following theorems:  You may use the following table for you calculations:
 
 
 
GF(33) defined by the primitive polynomial  p(x) = x3 + 2x + 1
Antilog Log Antilog Log
000 -INF
100  0 200 13
010  1 020 14
001  2 002 15
210  3 120 16
021  4 012 17
212  5 121 18
111  6 222 19
221  7 112 20
202  8 101 21
110  9 220 22
011 10 022 23
211 11 122 24
201 12 102 25


Problem 2.
 You will find below the Antilog/Log table of  GF(26)  based on the primitive polynomial

                                                 p(x) = x6 + x + 1

Use this table to compute the minimum polynomial  m5(x)  of  ksi5 , where  ksi  is the primitive element defined by  p(x).
 
Antilog Log Antilog Log Antilog Log Antilog Log
000000 -INF 000101 15 101001 31 111001 47
100000 0 110010 16 100100 32 101100 48
010000 1 011001 17 010010 33 010110 49
001000 2 111100 18 001001 34 001011 50
000100 3 011110 19 110100 35 110101 51
000010 4 001111 20 011010 36 101010 52
000001 5 110111 21 001101 37 010101 53
110000 6 101011 22 110110 38 111010 54
011000 7 100101 23 011011 39 011101 55
001100 8 100010 24 111101 40 111110 56
000110 9 010001 25 101110 41 011111 57
000011 10 111000 26 010111 42 111111 58
110001 11 011100 27 111011 43 101111 59
101000 12 001110 28 101101 44 100111 60
010100 13 000111 29 100110 45 100011 61
001010 14 110011 30 010011 46 100001 62
 


Last Modified: March 7, 1998