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

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Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-divisible linear codes spanned by codewords of weight Δ.
Bayreuth , 2023 . - 12 S.

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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. As an application, we give an alternative proof of a theorem of Liu on binary Δ-divisible codes of length 4Δ in the projective case.