Some new optimal quaternary constant weight codes

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 2k − 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.

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