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homework - addition. Calculate 6+2, 6-4 4) A canonical base...

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EE 421 – Fall 2010 Homework 1 Due Thursday October 14th Chapter 1 Given a (9,5) systematic code with equations: c i =m i i=0,1,2,3,4 c 5 =m 0 +m 1 +m 4 c 6 =m 1 +m 3 +m 4 c 7 =m 2 +m 3 c 8 =m 3 +m 4 encode the following messages: (00010), (00100),(11111),(10101) Chapter 2 1) Construct the operation table for the group of order 9 under modulo 9 addition. Calculate 3+7, 2+5, 8+8, 5-3 2) Construct the operation tables (addition and multiplication) for GF(13). Calculate 7*12+10, 11/5-7 3) Check if S={0,2,4,6} forms a subgroup of G={0,1,2,3,4,5,6,7} under modulo 8
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Unformatted text preview: addition. Calculate 6+2, 6-4 4) A canonical base for H 7 is {(0000001), (0000010), (0000100), (0001000), (0010000), (0100000), (1000000)}. Express the vector (1010111) as a linear combination of the elements of the canonical base. 5) A non canonical base for H 5 is {(00101), (10100), (11000), (11001), (01110)}. Express the vector (10101) as a linear combination of the elements of this non-canonical base. 6) Find a base for the (9,5) code in the first problem...
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