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01.06.2015 | Ausgabe 3/2015

Designs, Codes and Cryptography 3/2015

Hanani triple packings and optimal \(q\)-ary codes of constant weight three

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 3/2015
Autoren:
Yeow Meng Chee, Gennian Ge, Hui Zhang, Xiande Zhang
Wichtige Hinweise
Communicated by T. Etzion.

Abstract

The exact sizes of optimal \(q\)-ary codes of length \(n\), constant weight \(w\) and distance \(d=2w-1\) have only been determined for \(q\in \{2,3\}\), and for \(w|(q-1)n\) and \(n\) sufficiently large. We completely determine the exact size of optimal \(q\)-ary codes of constant weight three and minimum distance five for all \(q\) by establishing a connection with Hanani triple packings, and settling their existence.

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