Added some research notes

Author: jakewilliami

README.md

@@ -33,3 +33,4 @@ If *&Mellintrf; &SubsetEqual; &Sigma;<sup>k</sup>* is the set of messages, then
 ## A note on the number of codewords in a code
 
 We have some algorithms brute-force searching for the codewords in a [q, n, d]-code.  These algorithms are brute-force as they do not assume that q is a prime power.  Therefore, they go through all possible codewords of a [q, n]-code, and narrow down the code based on d.  There algorithms are namely `get_codewords_greedy` and `get_codewords_random`, both of which using `get_all_codewords`.  The `get_codewords` function iterates through possibilities of `get_codeword_random` and chooses the maximum of those iterations or the `get_codeword_greedy` length.  Despite the name, `get_codewords` is only a **probably** candidate.  Increate the keyword argument `m` to decrease the likelihood that there is a code with more codewords while maintaining the bound of the distance.  Furthermore, there is a `get_codewords` method that lists all linear combinations of rows of a generator matrix.
+

research.md

@@ -0,0 +1,14 @@
+<h1 align="center">Research</h1>
+
+A fair amount of research has gone into ensuring this is an accurate package.  However, I do believe I have only scratched the surface, as it were, of Coding Theory.  I have implemented some code bounds and distances, some polynomial/algebraic functions, but there is much more Coding Theory than is currently in the scope of this package.
+
+This package was actually created in an exploratory attempt at finding some interesting code spaces.  Here are some papers I found helpful in writing this:
+  - [Error detecting and error correcting codes (Hamming, 1950)](https://calhoun.nps.edu/bitstream/handle/10945/46756/Hamming_1982.pdf;jsessionid=027619D193DDF740A8CF4DAADBC9CF39?sequence=1);
+  - [Notes on digital coding (Golay, 1949)](https://www.lama.univ-savoie.fr/pagesmembres/hyvernat/Enseignement/1718/info607/TP-Golay/golay_paper.pdf);
+  - [A survey of perfect codes (van Lint; 1975)](https://projecteuclid.org/download/pdf_1/euclid.rmjm/1250130635);
+  - [Bounds on codes over an alphabet of five elements (Bogdanova & Östergård; 2001)](https://www.sciencedirect.com/science/article/pii/S0012365X00003836/pdf?md5=c0332c8c63996d1447bdef11a87af7dc&pid=1-s2.0-S0012365X00003836-main.pdf&_valck=1);
+  - [On the classification of MDS codes (Kokkala, Krotov, & Östergård; 2014)](https://ieeexplore.ieee.org/iel7/18/7331248/07294677.pdf);
+  - [Futher results on the classification of MDS codes (Kokkala & Östergård; 2015)](https://www.aimsciences.org/article/exportPdf?id=6c9701df-4372-46cf-acac-5ef9efdf4244);
+  - [An optimum nonlinear code (Nordstrom; 1968)](http://www.sciencedirect.com/science/article/pii/S0019995867908352/pdf?md5=b217d91216e8b2ddaa761dbed6107563&pid=1-s2.0-S0019995867908352-main.pdf);
+
+There doesn't seem to be much in the way of previous research/applications of Coding Theory in Julia.  There is [a paper by Ryan Quinn](https://dspace.sunyconnect.suny.edu/bitstream/handle/1951/70206/R%20Quinn%20MS%20Project%20document%2020180507.pdf?sequence=1&isAllowed=y) on the topic, but at time of writing, there isn't much else.  If others find this package useful, I woud love to see pull requests and extensions made from this package.