Using impartial games and greedy algorithms to generate codes with fixed distance

B−greedy codes are codes with a fixed distance, defined by a greedy algorithm. Despite simple construction, B−greedy codes possess many properties that are useful in the study of coding theory. A subset of these codes, known as lexicographic codes, or lexicodes for short, has connections with impartial games, making them even more fruitful to study. By studying impartial games, we gain access to additional tools that can be used to study lexicodes, as winning positions in impartial games are related to codewords in lexicodes. This paper aims to study lexicodes in the context of Sprague-Grundy analysis and highlight the connection between winning strategies and greedy algorithms. We will also present a proof of the Gilbert-Varshamov bound using B−greedy codes.