Year: 2017
Type: book-chapter
Abstract: For which positive integers $n,k,r$ does there exist a linear $[n,k]$ code $C$ over $\mathbb{F}_q$ with all codeword weights divisible by $q^r$ and such that the columns of a generating matrix of $C$ are projectively distinct? The motivation for studying this problem comes from the theory of partial spreads, or subspace codes with the highest possible minimum distance, since the set of holes of a partial spread of $r$-flats in $\operatorname{PG}(v-1,\mathbb{F}_q)$ corresponds to a $q^r$-divisible code with $k\leq v$. In this paper we provide an introduction to this problem and report on new results for $q=2$.
Authors: Heinlein, Daniel, Honold, Thomas, Kiermaier, Michael, Kurz, Sascha, Wassermann, Alfred
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2603600196