Some new optimal quaternary constant weight codes

Abstract

Constant weight codes (CWCs) are an important class of codes in coding theory. Generalized Steiner systems GS(2, k , v , g ) were first introduced by Etzion and used to construct optimal nonlinear CWCs over an alphabet of size g +1 with minimum Hamming distance 2 k −3, in which each codeword has length v and weight k . In this paper, Weil's theorem on character sum estimates is used to show that there exists a GS(2,4, v ,3) for any prime v ≡ 1 ( mod 4) and v >13. From the coding theory point of view, an optimal nonlinear quaternary ( v ,5,4) CWC exists for such a prime v .