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- Marcelo Firer, Judy L. Walker
- IEEE Transactions on Information Theory
- 2016

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this paper, we study channels and metrics for which those two criteria do and do not… (More)

- Luciano Panek, Marcelo Firer, Hyun Kwang Kim, Jong Yoon Hyun
- Discrete Mathematics
- 2008

- Jerry Anderson Pinheiro, Marcelo Firer
- IEEE Transactions on Information Theory
- 2012

In this paper, 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 same dimension. When the poset-block admits the MacWilliams-type identity, we explicitly state the relation between the weight enumerators of a code and its dual.

- Alexander Barg, Marcelo Firer, Marcos Vinicius Spreafico, Luciano Vianna Felix
- Discrete Mathematics
- 2014

We investigate linear and additive codes in partially ordered Hamming-like spaces that satisfy the extension property, meaning that automorphisms of ideals extend to automorphisms of the poset. The codes are naturally described in terms of translation association schemes that originate from the groups of linear isometries of the space. We address questions… (More)

- Luciano Panek, Marcelo Firer, Marcelo Muniz Silva Alves
- IEEE Trans. Information Theory
- 2010

- Luciano Vianna Felix, Marcelo Firer
- Adv. in Math. of Comm.
- 2012

- Allan De Oliveira Moura, Marcelo Firer
- IEEE Transactions on Information Theory
- 2010

In this paper, we extend Wei's Duality Theorem, relating the generalized Hamming weight hierarchy of a code to the hierarchy of the dual code, to the scope of codes with poset metrics. As a consequence of this duality theorem, we prove some results concerning discrepancy of codes and chain condition for generalized weights.

- Marcelo Muniz Silva Alves, Luciano Panek, Marcelo Firer
- Adv. in Math. of Comm.
- 2008

- Rafael Gregorio Lucas D'Oliveira, Marcelo Firer
- 2014 IEEE International Symposium on Information…
- 2014

Considering a poset metric as a generalization of Hamming's metric, the packing radius of a code is not necessarily a function of the minimal distance. In this work we show, without any restriction on the poset, that the relation between the weight and the packing radius of a vector is equivalent to a generalization of the classical partition problem. We… (More)

- Roberto Assis Machado, Jerry Anderson Pinheiro, Marcelo Firer
- IEEE Transactions on Information Theory
- 2017

In this paper, we consider metrics determined by hierarchical posets and give explicit formulas for the main parameters of a linear code: the minimum distance and the packing, covering, and Chebyshev radii of a code. We also present ten characterizations of hierarchical poset metrics, including new characterizations and simple new proofs to the known ones.