Name: Completely decomposable rank-metric codes
Creator: Paolo Santonastaso
Keywords: FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2025Embargo end date: 01 Jan 2024 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 726, pages 371-404 (issn: 0024-3795,

Authors: Paolo Santonastaso;

doi: 10.1016/j.laa.2025.07.037 , 10.48550/arxiv.2406.19026

arXiv: http://arxiv.org/abs/2406.19026

Completely decomposable rank-metric codes

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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.

Keywords

FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT)

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