The Partition Weight Enumerator of MDS Codes and its Applications
Mostafa El-Khamy, Robert J. McEliece
TL;DR
This paper derives a closed-form formula for the partition weight enumerator of MDS codes, explores their properties, extends results to binary images, and applies findings to analyze multiuser error probability in Reed Solomon codes.
Contribution
It provides the first closed-form formula for the partition weight enumerator of MDS codes and extends the analysis to their binary images, with applications to Reed Solomon codes.
Findings
Closed-form formula for partition weight enumerator of MDS codes
Properties of MDS codes discussed using the new formula
Analysis of multiuser error probability for Reed Solomon codes
Abstract
A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for the average binary image of MDS codes in finite fields of characteristic two. As an application, we study the multiuser error probability of Reed Solomon codes.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Wireless Communication Techniques · Error Correcting Code Techniques