Two-weight rank-metric codes
Ferdinando Zullo, Olga Polverino, Paolo Santonastaso, John Sheekey
TL;DR
This paper characterizes two-weight linear codes in the rank metric, expanding understanding of their structure and potential applications, and addresses a recent open question in the field.
Contribution
It provides a complete characterization of two-weight rank-metric codes, answering a recent open problem and extending the theory beyond Hamming metric codes.
Findings
Characterization of two-weight rank-metric codes
Connection to applications like secret sharing and association schemes
Addresses a recent open question in coding theory
Abstract
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we characterize two-weight codes in the rank metric, answering a recent question posed by Pratihar and Randrianarisoa.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding