2015/03/09 by Johan P. Hansen, Hansen, Johan P.
Computer Science · Mathematics · #68M10 #90B18 #94A05 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT #msc:68M10 #msc:90B18 #msc:94A05
paper · pdf · doi:10.48550/arxiv.1503.02386
8 pages
arxiv created 2015/03/09 · openalex publication_date 2015/03/09 · arxiv updated 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated with the Suzuki and Ree groups all having the maximal number of points for curves of their respective genera. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang %\citeDBLP:journals/tit/KoetterK08 introduced a metric on the set of vector spaces and showed that a minimal distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The vector spaces in our construction have minimal distance bounded from below in the above metric making them suitable for linear network coding.