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Huffman and Pless: Fundamentals of Error-Correcting Codes.

You may also find Lindell's lecture notes (available from his course home page) useful.

The exam will be on May 15, with permitted aids code C. Previous exams are available.

Chapters from the book:

• 1.1-1.8, 1.10, 1.12.
• 2.1, 2.4, 2.8.
• 3.1-3.7
• 4.1-4.5
• 5.1-5.2, 5.4.1, 5.4.2
• 14.1-14.5

Notes:

• Reed-Muller codes
• Convolutional codes

For some of the exercises, you will need to read material from the book that has not been covered in the lectures.

There will be no specific exercise class this spring. If you need help with any of the exercises, send me an e-mail or drop by my office.

These are exercises that you probably need computer assistance to solve.

Consider a binary cyclic code of length 127 with generator polynomial

x^28 + x^27 + x^23 + x^21 + x^18 + x^16 + x^14 + x^13 + x^12 + x^11 + x^8 + x^5 + x^4 + x^3 + x^2 + x + 1

• What is its zero set, relative to an \(\alpha\) of order 127 satisfying \(\alpha^7 = \alpha+1\)?
• What is its dimension and minimum distance?

Suppose you have received

x^33 + x^32 + x^31 + x^30 + x^29 + x^23 + x^22 + x^19 + x^18 + x^17 + x^12 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^2 + 1

• What is the nearest code word?
• If the code word was encoded as \(m(x)g(x)\), find \(m(x)\).

This plan will change.