Linear Erasure Block Codes over Either a Field of Rational Numbers Q or an Algebraic Structure Ψq

Abstract

In this paper, we define a mathematical model of linear erasure block codes (k, C) for symbol erasure channels (SEC) that are built over either a field of rational numbers $Q$ or an algebraic structure $\pmb{\Psi q}$. We show the necessary condition for the codes (k, C) to be optimal, and we demonstrate that some of the already existing erasure codes may be considered as the specific cases of the codes (k, C) over a $\pmb{\Psi_{q}}$, such as Luby Transform, Raptor or Zigzag Decodable.