2015/10/08 by Qifu Tyler Sun, Shuo-Yen Robert Li, Zongpeng Li · 11 citations
Computer Science · Mathematics · #Algebraic number #Base (topology) #Cooperative Communication and Network Coding #Coset #Finite Group Theory Research #Finite field #Interconnection Networks and Systems #Linear network coding #Multicast #Multiplicative function #Topology (electrical circuits) #cs.IT #math.IT
paper · pdf · doi:10.1109/tit.2016.2613988
published in IEEE Transactions on Information Theory 62(12), 7272-7282 (Institute of Electrical and Electronics Engineers) · 29 pages, 5 figures
arxiv created 2015/10/08 · openalex publication_date 2016/09/27 · openalex created_date 2016/10/07 · arxiv updated 2017/12/18 · openalex updated_date 2026/08/05
For a (single-source) multicast network, the size of a base field is the most known and studied algebraic identity that is involved in characterizing its linear solvability over the base field. In this paper, we design a new class N of multicast networks and obtain an explicit formula for the linear solvability of these networks, which involves the associated coset numbers of a multiplicative subgroup in a base field. The concise formula turns out to be the first that matches the topological structure of a multicast network and algebraic identities of a field other than size. It further facilitates us to unveil infinitely many new multicast networks linearly solvable over GF(q) but not over GF(q') with q2k) but not over GF(22k+1) and 2) for arbitrary distinct primes p and p', there are infinitely many k and k' such that an instance in N can be found linearly solvable over GF(pk) but not over GF(p'k') with pkk'.