Title:
Classification of Δ-divisible linear codes spanned by codewords of
weight Δ

Abstract:
We classify all q-ary Δ-divisible linear codes which are spanned by
codewords of weight Δ. The basic building blocks are the simplex codes,
and for q=2 additionally the first order Reed-Muller codes and the
parity check codes.
This generalizes a result of Pless and Sloane, where the binary
self-orthogonal codes spanned by codewords of weight 4 have been
classified, which is the case q=2 and Δ=4 of our classification.