1. Encode 11011100001 using x⁴ + x + 1 (mod x¹⁵ + 1)
2. Decode 101100101011000 using the same code.
3. Let a be the element x²+1 in Z₂[x]/(x⁴+x³+x²+x+1). Find the minimal polynomial p_a(z) for a over Z₂.
4. Let F,K be fields with F contained in K. Let a be an element of K and let p_a(x) be the minimal polynomial of a over F. Show that p_a(x) is irreducible over F.
5. Does x⁷+x⁶+4x+3 have any double roots (in the complex plane C)?

More Information

• "A Tale of Two Sieves" by Carl Pomerance. This is an expository article aimed at mathematicians who are not familiar with factoring algorithms. Parts of it should be very readable for you (and other parts more challenging). You need the Adobe Acrobat Reader to view this article. This plug-in is freely available and should be installed on all public machines on campus.
• Download UBASIC software. You will need a utility to unzip the ub874.zip file. If you haven't installed software from a zip file before you may want to get help from someone who has. The readme file isn't particularly helpful, but the ubhelp.doc file is useful.
• Download Aladdin Expander. This is my favorite file decompression product because it handles files compressed both on PC's and on Mac's (and it is free). Once you download the product, you double click on it to install, then just drag and drop the file you want to expand.
• RSA patent released
• Course Outline
• Lecture Notes
• Help Sessions
• Old Assignments
• Andrew G. Bennett's Home Page