2015/12/21 by Thomas Honold, Honold, Thomas, Kiermaier, Michael +2
Computer Science · Engineering · #05B25 #51E14 #51E20 (Primary) #51E22 #51E23 (Secondary) #94B05 #Advanced Wireless Communication Technologies #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1512.06660
openalex publication_date 2015/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Codes in finite projective spaces equipped with the subspace distance have been proposed for error control in random linear network coding. The resulting so-called Main Problem of Subspace Coding is to determine the maximum size Aq(v,d) of a code in PG(v-1,\mathbbFq) with minimum subspace distance d. Here we completely resolve this problem for d≥ v-1. For d=v-2 we present some improved bounds and determine Aq(5,3)=2q3+2 (all q), A2(7,5)=34. We also provide an exposition of the known determination of Aq(v,2), and a table with exact results and bounds for the numbers A2(v,d), v≤ 7.