# Non-Projective Two-Weight Codes

## TL;DR

This paper explores non-projective two-weight codes and shows that their weight differences follow a specific mathematical pattern under certain conditions.

## Contribution

The paper extends the known result about weight differences in two-weight codes to non-projective cases with mild conditions.

## Key findings

- The difference of non-zero weights in non-projective two-weight codes is a power of the field's characteristic under mild conditions.
- Exhaustive enumerations of feasible parameters are provided for small dimensions in the binary case.

## Abstract

It has been known since the 1970’s that the difference of the non-zero weights of a projective Fq-linear two-weight code 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.