2015/06/12 by Umberto Martínez-Peñas, Martínez-Peñas, Umberto · 1 citation
Computer Science · Engineering · #94B05 #94B65 #94C99 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Full-Duplex Wireless Communications #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.1506.04036
openalex publication_date 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Rank weights and generalized rank weights have been proven to characterize error and erasure correction, and information leakage in linear network coding, in the same way as Hamming weights and generalized Hamming weights describe classical error and erasure correction, and information leakage in wire-tap channels of type II and code-based secret sharing. Although many similarities between both cases have been established and proven in the literature, many other known results in the Hamming case, such as bounds or characterizations of weight-preserving maps, have not been translated to the rank case yet, or in some cases have been proven after developing a different machinery. The aim of this paper is to further relate both weights and generalized weights, show that the results and proofs in both cases are usually essentially the same, and see the significance of these similarities in network coding. Some of the new results in the rank case also have new consequences in the Hamming case.