Non-projective two-weight codes

Abstract

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.

arXiv comment27 pages, 14 tables, appendix on parameters of projective two-weight codes added