Divisible Codes

12/22/2021

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by   Sascha Kurz, et al.

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A linear code over 𝔽_q with the Hamming metric is called Δ-divisible if the weights of all codewords are divisible by Δ. They have been introduced by Harold Ward a few decades ago. Applications include subspace codes, partial spreads, vector space partitions, and distance optimal codes. The determination of the possible lengths of projective divisible codes is an interesting and comprehensive challenge.