On the construction of nonbinary constant-weight codes

Abstract

Constant-weight codes play an important role in coding theory. Binary constant-weight codes have been extensively investigated. Nonbinary constant-weight codes have also attracted recent attention due to several important applications requiring nonbinary alphabets. However, they are still much less understood than binary constant-weight codes. In this thesis, we make a thorough study on known constructions of nonbinary constant- weight codes, and provide new constructions for two in fite families of optimal codes. The first construction shows that Aq(n, 2w - 1, w) = (q - 1)n/w for all sufficiently large n satisfying w|(q - 1)n. The second construction uses a novel idea based on sequences to construct optimal q-ary (q, 4, 3)-codes for all q >= 3.