Stopping Sets of Algebraic Geometry Codes over Hyperelliptic Curves of Genus Two - Abdulla Eid (Mathematics)
Stopping sets are useful for analyzing the performance of a linear code under an iterative decoding algorithm over an erasure channel. In this paper, we consider stopping sets of one-point algebraic geometry codes defined by a hyperelliptic curve of genus <semantics>g=2</semantics> defined by the plane model <semantics>y2=f(x)</semantics>, where the degree of <semantics>f(x)</semantics> was 5. We completely classify the stopping sets of the one-point algebraic geometric codes <semantics>C=CΩ(D,mP∞)</semantics> defined by a hyperelliptic curve of genus 2 with <semantics>m≤4</semantics>. For <semantics>m=3</semantics>, we proved in detail that all sets <semantics>S⊆{1,2,⋯,n}</semantics> of a size greater than 3 are stopping sets and we give an example of sets of size <semantics>2,3</semantics> that are not.