A note on the generalized Hamming weights of Reed-Muller codes
Peter Beelen
TL;DR
This paper provides a simplified description of the generalized Hamming weights of Reed-Muller codes by extending the Macaulay representation of integers.
Contribution
It introduces a generalized Macaulay representation to analyze the generalized Hamming weights of Reed-Muller codes.
Findings
Simplified characterization of generalized Hamming weights
Extension of Macaulay representation for integers
Basic properties of the generalized representation
Abstract
In this note, we give a very simple description of the generalized Hamming weights of Reed--Muller codes. For this purpose, we generalize the well-known Macaulay representation of a nonnegative integer and state some of its basic properties.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cryptographic Implementations and Security