Math Extended Essay!!!

[Ram_A]

Hi, I decided to do a math EE on factors that determine the strengths of a Linear Feedback Shift Register. I thought I would talk about the seed, taps and the number of flip-flop and do many statistical test, however half way through my research I came to realize that the only thing that affects the strength is the taps and thus there wouldn’t be much of exploration except some simple things about finite fields. Nonetheless I have already written quarter of the essay on stream ciphers and LFRS, and also for most of my break I was reading about LFSRs, so I don’t want that to go to waste. Can someone help me by suggesting a thing that I could explore for my EE that still be related to LFSR.

Thank you

[kw0573]

LFSR seems have a lot of math at or beyond the HL level. However, in Math HL EE, you do not talk about statistical tests unless there is no better way to discuss the topic (that is, unless you are discussing statistics). In this case, set theory and number theory may be better as you deal with XOR function, truth tables, and "exclusively and" functions. If you resort to statistics to explain math that can be explained by other branches of math, then you are not fully demonstrating your math knowledge. 

In any EE, your goal is not to simply explain some topic but to demonstrate that you know exactly what you are explaining. In the latter group, you can easily answer the following: Why are LFSR defined as such? What is its significances, in terms of mathematics and applications? What interesting properties does it have? What are some alternative functions to generate a close loop of finite number of terms? What are some advantages/disadvantages to defining LFSR such way, and how does it compare to similar functions?

Hope you can finetune your research question soon. Message me if you have any further inquiries. 

Edited July 28, 2016 by kw0573