Constant dimension codes from Riemann-Roch spaces (Q1691237)

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. Then the involved codewords vector spaces. A subspace code \(C\) is a subset of the set of all subspaces of \(\mathbb{F}_q^N\). When all the subspaces of \(C\) have a fixed dimension then \(C\) is called constant dimension code. In [\textit{J. P. Hansen}, Int. J. Math. Comput. Sci. 10, No. 1, 1--11 (2015; Zbl 1384.94124)], the author presented a family of constant dimension linear network codes using algebraic curves over finite fields and certain Riemann-Roch spaces associated to divisors constructed from their rational points. In this article, the construction of Hansen is generalized to three families of codes, also of constant dimension. The three families are obtained by relaxing the conditions originally imposed by Hansen, which allows greater flexibility and variety. The parameters of the obtained codes are studied. Finally the authors give some numerical computations on the rates of the three families, showing the performance of these codes.