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hw1_810

# hw1_810 - and so forth will be treated with great...

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Math 810, Spring 2011 – HW 1 Due Friday, 4 February 2011 You may talk with each other about problems but make sure you write up your solutions separately. Make sure you explain things carefully. Some remarks: 1. Most problems that you will get this semester are not very diﬃcult. Please try to solve the problems without looking them up in books, on the net, or whatever. 2. Examples and pictures can be of help in supporting or motivating an ar- gument, but they do not constitute proofs. 3. “I wrote a computer program that said this.” is not a valid proof. 4. Statements such as “it is trivial,” “it is easy,” “by a similar argument,”
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Unformatted text preview: and so forth will be treated with great skepticism. 1. Problem 2.2.2 from the Notes : http://www.math.msu.edu/~jhall/classes/codenotes/coding-notes.html 2. Problem 2.2.4 from the Notes . 3. I have a 1-error-correcting code code C in { , 1 } 5 , and I know that there is no other 1-error-correcting code D in { , 1 } 5 with | D | > | C | . ( a ) Use the Sphere Packing Bound and the Gilbert-Varshamov Bound to ﬁnd a lower and an upper bound on | C | . ( b ) Give an example of a 1-error-correcting code E in { , 1 } 5 with | E | = | C | . (Make sure you prove that your code has the largest possible size.)...
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