We give a gentle introduction to the famous and longstanding MDS Conjecture, which was posed by Segre in 1955, and asks: What is the maximum number of vectors in a k-dimensional vector space over F_q that you can have such that any k vectors form a basis? We also introduce the necessary tools for understanding Simeon Ball's 2010 proof of the MDS conjecture for prime fields, which is the most important work on the conjecture to date.
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