Computation of the Weight Distribution of CRC Codes
Felice Manganiello
TL;DR
This paper presents an efficient algorithm for computing the weight distribution of CRC codes and their duals, leveraging recursive structures and MacWilliams Theorem to improve upon standard enumeration methods.
Contribution
The paper introduces a novel recursive algorithm that simplifies weight distribution computation for CRC codes and their duals, avoiding exhaustive listing.
Findings
The algorithm efficiently computes weight distributions for CRC codes.
It leverages recursive structures and MacWilliams Theorem.
It outperforms standard enumeration methods.
Abstract
In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from just some ``representative'' words. Thanks to MacWilliams Theorem, the computation of the weight distribution of dual codes can be easily brought back to that of CRC codes. This algorithm is a good alternative to the standard algorithm that involves listing every word of the code.
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Taxonomy
TopicsCoding theory and cryptography · Digital Filter Design and Implementation · Advanced Wireless Communication Techniques