A linear code over $\mathbb{F}_q$ with the Hamming metric is called $\Delta$-divisible if the weights of all codewords are divisible by $\Delta$. 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.

翻译：设$\mathbb{F}_q$上具有汉明度量的线性码，若其所有码字重量均可被$\Delta$整除，则称为$\Delta$-可除码。此类码由Harold Ward于数十年前提出，其应用涵盖子空间码、部分扩域、向量空间划分及距离最优码。确定射影可除码的可能长度是一项有趣且具综合性挑战的课题。