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math.AC2024
Coarsest Fourier-reflexive Partitions for the Lee, Homogeneous and Subfield Metric
Jessica Bariffi, Giulia Cavicchioni, Violetta Weger
MacWilliams identities relate the weight enumerators of a code with those of its dual and are classically formulated with respect to the Hamming weight. For other metrics, however,…
cs.IT2024
Bounds on Sphere Sizes in the Sum-Rank Metric and Coordinate-Additive Metrics
Hugo Beeloo-Sauerbier Couvée, Thomas Jerkovits, Jessica Bariffi
This paper provides new bounds on the size of spheres in any coordinate-additive metric with a particular focus on improving existing bounds in the sum-rank metric. We derive impro…