Second weight codewords of generalized Reed-Muller codes
Elodie Leducq
TL;DR
This paper characterizes the second weight codewords in generalized Reed-Muller codes, providing insights into their structure and weight distribution for codes of a specific order and length.
Contribution
It explicitly determines the second weight codewords of generalized Reed-Muller codes, a previously unresolved aspect of their weight hierarchy.
Findings
Identifies the second weight codewords explicitly
Provides a detailed description of their structure
Enhances understanding of code weight distribution
Abstract
In this paper we give the second weight codewords of the generalized Reed-Muller code of order r and length .
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications