Completely decomposable rank-metric codes
Paolo Santonastaso
TL;DR
This paper explores the structure and properties of completely decomposable rank-metric codes, focusing on their weight distribution and classification of codes with many minimum weight codewords.
Contribution
It provides a detailed analysis of the weight distribution and classification of completely decomposable rank-metric codes, a novel subclass of rank-metric codes.
Findings
Characterization of codewords with specific rank weights
Classification of codes with maximum minimum weight codewords
Insights into the structure of decomposable rank-metric codes
Abstract
In this paper, we investigate completely decomposable rank-metric codes, i.e. rank-metric codes that are the direct sum of 1-dimensional maximum rank distance codes. We study the weight distribution of such codes, characterizing codewords with certain rank weights. Additionally, we obtain classification results for codes with the largest number of minimum weight codewords within the class of completely decomposable codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Rings, Modules, and Algebras