Construction of several classes of maximum codes.

Let A (n , d) be the size of the maximum binary code of length n and minimum Hamming distance d. A (n , d , w) is defined similarly for binary code with constant weight w. Obviously, finding the value of A (n , d) is equivalent to finding the maximum independent set of the d − 1 th-power of n -dimensional hypercube. Based on this, this paper obtains that A (3 m , 2 m) = 4 , A (m (m + 1) 2 , 2 m − 2 , m) = m + 1 , A (2 m + 1 − 2 , 2 m − 1) = 2 m + 1 , and explores the structure of the maximum code of length 2 m + 2 and minimum Hamming distance 2 m + 1 , where m is an integer. [ABSTRACT FROM AUTHOR]