hw-4-2009 - A Range Problems 1 • 4 Roth text problem 4.14...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 556: Coding Theory, 2009 HW 4 Issued: October 5th, 2009 Due: October 15th, 2009 October 5, 2009 A- range Problems 1) Show that over any finite field of order q and characteristic p , one has ( x + y ) p = x p + y p . (1) 2) Roth text, problem 4.29. 3) Consider the code with H matrix given by: H = [ H 1 I 3 × 3 ] , (2) where H 1 is the parity check matrix of the [7 , 4 , 3] Hamming code. Give an interpretation of this code, i.e. give a shorthand description of its codewords, and show how this leads to the weight enumerator quickly. To calculate the exact probability of error for signaling, assuming that we have a ML decoder and that the transmission is over a BSC, we must know the weights of the coset leaders. Find these as well. Remark : Do not use a computer to solve this problem.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: A Range Problems 1 • 4) Roth text, problem 4.14. You are allowed to search online for perfect ternary codes. • 5) SVHITDXEHOERCPRUOEERASTNPBMOHTFTLTFSNIETRLFMAEO The space symbols are not encrypted. A+ Range Problems • 6) The covering radius of a code is the largest weight of a coset leader of the code. What can you say about the covering radius of perfect codes? Can you find an upper bound on the covering radius of an arbitrary linear block code? The covering radius of codes that meet the Singleton bound, Griesmer bound (i.e. can you tell if there is any connection at all between the covering radius and the bounds at hand)? 2...
View Full Document

This note was uploaded on 02/08/2012 for the course ECE 556 taught by Professor Milenkovic,o during the Fall '08 term at University of Illinois, Urbana Champaign.

Page1 / 2

hw-4-2009 - A Range Problems 1 • 4 Roth text problem 4.14...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online