17 citations · 18 across the 4 of their papers we have counts for
6 papers
Canonical form of linear subspaces and coding invariants: the poset metric point of view
Jerry Anderson Pinheiro, Marcelo Firer
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordi…
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…
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…
Coding and Decoding Schemes for MSE and Image Transmission
Marcelo Firer, Luciano Panek, Jerry Anderson Pinheiro
In this work we explore possibilities for coding and decoding tailor-made for mean squared error evaluation of error in contexts such as image transmission. To do so, we introduce…
Bounds for complexity of syndrome decoding for poset metrics
Marcelo Firer, Jerry Anderson Pinheiro
In this work we show how to decompose a linear code relatively to any given poset metric. We prove that the complexity of syndrome decoding is determined by a maximal (primary) suc…
Classification of poset-block spaces admitting MacWilliams-type identity
Jerry Anderson Pinheiro, Marcelo Firer
In this work we prove that a poset-block space admits a MacWilliams-type identity if and only if the poset is hierarchical and at any level of the poset, all the blocks have the sa…