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 g = 2 defined by the plane model y2 = f (x), where the degree of f (x) was 5. We completely classify the stopping sets of the one-point algebraic geometric codes C = CΩ(D,mP∞) defined by a hyperelliptic curve of genus 2 with m ≤ 4. For m = 3, we proved in detail that all sets S ⊆ {1, 2, . . . , n} of a size greater than 3 are stopping sets and we give an example of sets of size 2, 3 that are not.
Loading....