It has been known since the 1970's that the difference of the non-zero weights of a projective $\mathbb{F}_q$-linear two-weight has to be a power of the characteristic of the underlying field. Here we study non-projective two-weight codes and e.g.\ show the same result under mild extra conditions. For small dimensions we give exhaustive enumerations of the feasible parameters in the binary case.

翻译：自1970年代以来，人们已知射影$\mathbb{F}_q$线性二重量码的非零权重之差必须为底层域特征数的幂。本文研究非射影二重量码，并在温和的附加条件下证明相同结论。对于小维度，我们给出二进制情形下可行参数的穷举枚举。