An asymptotic property of quaternary additive codes

The article delves into the geometric properties of quaternary additive codes, a generalization of linear codes, and their connection to quantum stabilizer codes. It introduces the concept of dimension for these codes and defines the maximal length of such codes for given parameters. The main result is the construction of a family of constant-weight codes that are optimal in terms of length and dimension. Additionally, the article presents a variant construction that yields an interesting infinite family of additive codes. Throughout, the article uses geometric language to study these codes and establishes new existence conditions based on the Griesmer bound.