2017/03/24 by Daniel Heinlein, Thomas Honold, Heinlein, Daniel +7
Computer Science · Engineering · Mathematics · #51E23 #94B05 #Arithmetic #Binary number #Coding theory and cryptography #Combinatorics (math.CO) #Discrete mathematics #FOS: Mathematics #Finite Group Theory Research #Mathematics #Projective test #Pure mathematics #graph theory and CDMA systems #math.CO #msc:51E23 #msc:94B05
paper · pdf · doi:10.48550/arxiv.1703.08291
10 pages, 3 tables
arxiv created 2017/03/24 · openalex publication_date 2017/03/24 · arxiv updated 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For which positive integers n,k,r does there exist a linear [n,k] code C over \mathbbFq with all codeword weights divisible by qr 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 PG(v-1,\mathbbFq) corresponds to a qr-divisible code with k≤ v. In this paper we provide an introduction to this problem and report on new results for q=2.