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HerA Scheme: Secure Distributed Matrix Multiplication via Hermitian Codes
Roberto A. Machado, Gretchen L. Matthews, Welington Santos
We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of honest but curiou…
Root of Unity for Secure Distributed Matrix Multiplication: Grid Partition Case
Roberto Assis Machado, Felice Manganiello
We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of honest but curiou…
Field Trace Polynomial Codes for Secure Distributed Matrix Multiplication
Roberto Assis Machado, Rafael G. L. D'Oliveira, Salim El Rouayheb +1
We consider the problem of communication efficient secure distributed matrix multiplication. The previous literature has focused on reducing the number of servers as a proxy for mi…
Weights which respect support and NN-decoding
Roberto Assis Machado, Marcelo Firer
In this work we explore a family of metrics over finite fields which respect the support of vectors. We show how these metrics can be obtained from the edge-weighted Hamming cube a…
Combinatorial metrics: MacWilliams-type identities, isometries and extension property
Jerry Anderson Pinheiro, Roberto Assis Machado, Marcelo Firer
In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that…
Metrics Based on Finite Directed Graphs and Coding Invariants
Tuvi Etzion, Marcelo Firer, Roberto Assis Machado
Given a finite directed graph with vertices, we define a metric on , where is the finite field with elements. The weight of a word is d…
Characterization of metrics induced by hierarchical posets
Roberto Assis Machado, Jerry Anderson Pinheiro, Marcelo Firer
In this paper we consider metrics determined by hierarchical posets and give explicit formulae for the main parameters of a linear code: the minimum distance and the packing, cover…