Complexity of Error-Correcting Codes Derived from Combinatorial Games

The main result of the present paper is to establish an algorithm for computing a linear error-correcting code called lexicode in O(n d − 1) steps, where n and d are the size and distance of the code, respectively. This is done by using the theory of combinatorial games, specifically, two-player cellular automata games. Previous algorithms were exponential in n.