A Note on One Weight and Two Weight Projective $\mathbb {Z}_{4}$ -Codes

In this paper, we solve the open problems raised in <xref ref-type="bibr" rid="ref8">[8]</xref> and present some examples to illustrate the obtained results. Moreover, we work out the diophantine problem by Shi and Wang and then give the sufficient conditions for the nonexistence of two-Lee weight projective codes over <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{4}$ </tex-math></inline-formula> with type <inline-formula> <tex-math notation="LaTeX">$4^{k_{1}}2^{k_{2}}$ </tex-math></inline-formula>.

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