On perfect constant weight codes (Q2717201)

Generalizing a construction of \textit{J. H. van Lint} and \textit{L. Tolhuizen} [Design, Codes, and Cryptography 18, 231-234 (1999; Zbl 0963.94038)], the authors consider perfect single error-correcting codes of length \(n\) over the alphabet \(Q\) of \(2^k+1\) symbols, \(k\geq 1\) (note that \(k=1\) was handled in [loc. cit.]). The main result of the paper, which is proved making use of the cyclic \(t\)-ary Hamming code, is Theorem 1:NEWLINENEWLINENEWLINELet \(t= 2^k\), \(w= t+1\), and \(n= w+1\). There exists a perfect single error-correcting constant weight code of length \(n\) and weight \(w\) over an alphabet of size \(w\).NEWLINENEWLINENEWLINEThe paper ends with a look at quaternary codes.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00079].