Create a correctable code for a list of key words.  Your task is to create an efficient, correctable code for a list that contains 20 key words.  The words in your code will be represented as binary strings using only 0’s and 1’s.  Stringent correctability requirements mean your code must have a minimum distance of 3.

– Read Section 5.2 (pages 150-152) and understand the definitions for bit, binary word, code, codewords, Hamming distance, and minimum distance of a code.

– Create a code consisting of binary codewords.

– The code must meet three requirements

  — Contain at least 20 codewords

  — Have a minimum distance of 3 (explain why a min distance of 4 is no better than 3)

  — Maintain efficiency by using the fewest number of bits per codeword as possible

– Clearly document and describe your code: what it is, why you chose it, etc.

– Discuss how topology relates to the selection of your code and the Hamming metric

 

A few notes about format: use MS PowerPoint for your presentation; develop a presentation that is 10-15 slides in length; incorporate audio files into your presentation in order to explain your work; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and select fonts, backgrounds, etc. to make your presentation look professional.

 

Text Book: Adams-C-Franzosa-R-introduction-to-Topology-Pure-and-Applied-Prentic-Hall-2007