Stopping Sets of Algebraic Geometry Codes
Jun Zhang, Fang-Wei Fu, Daqing Wan

TL;DR
This paper analyzes the stopping sets and their distributions in algebraic geometry codes, especially from elliptic curves, to improve understanding of their decoding performance.
Contribution
It provides new characterizations of stopping sets for residue AG codes, including elliptic curve codes, linking the problem to subset sum problems in elliptic curve groups.
Findings
Complete characterization of stopping sets for elliptic curve AG codes
Reduction of stopping set analysis to subset sum problems in elliptic curve groups
Determination of stopping set distributions for specific elliptic curve codes
Abstract
Stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code. Let be an linear code over with parity-check matrix , where the rows of may be dependent. Let denote the set of column indices of . A \emph{stopping set} of with parity-check matrix is a subset of such that the restriction of to does not contain a row of weight 1. The \emph{stopping set distribution} enumerates the number of stopping sets with size of with parity-check matrix . Denote the parity-check matrix consisting of all the non-zero codewords in the dual code . In this paper, we study stopping sets and stopping set distributions of some residue algebraic geometry (AG) codes with parity-check matrix…
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Taxonomy
TopicsError Correcting Code Techniques · Cooperative Communication and Network Coding · Coding theory and cryptography
