Construction of several classes of maximum codes

Abstract

Let [Formula: see text] be the size of the maximum binary code of length [Formula: see text] and minimum Hamming distance [Formula: see text]. [Formula: see text] is defined similarly for binary code with constant weight [Formula: see text]. Obviously, finding the value of [Formula: see text] is equivalent to finding the maximum independent set of the [Formula: see text]th-power of [Formula: see text]-dimensional hypercube. Based on this, this paper obtains that [Formula: see text], [Formula: see text], [Formula: see text], and explores the structure of the maximum code of length [Formula: see text] and minimum Hamming distance [Formula: see text], where [Formula: see text] is an integer.