Following standard notation, an (n, m, d) code C denotes a binary code C which has length n, size m, and Hamming distance d. According to Hill  the “main coding theory problem” is to optimize one of these three parameters when the other two are held fixed. The usual version of this optimization problem is to find the largest code for a given length and given minimum distance. This is the problem we shall consider, thus making it clear what we mean by an “optimal code.”
Gary R. Greenfield. Simulated Annealing and Optimal Codes. Technical paper (TR-93-02). Math and Computer Science Technical Report Series. Richmond, Virginia: Department of Mathematics and Computer Science, University of Richmond, March, 1993.
Copyright © 1993, Gary R. Greenfield, University of Richmond, Richmond, Virginia.
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