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It has been known since the 1970's that the difference of the non-zero weights of a projective Fq-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.
Sascha Kurz (Mon,) studied this question.
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