1 citations · 2 across the 7 of their papers we have counts for
10 papers · 1 filter
The Generalized Covering Radii of Linear Codes
Dor Elimelech, Marcelo Firer, Moshe Schwartz
Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of linear codes -- the generalized cover…
Alternative Metrics
Marcelo Firer
The main scope of this chapter is metrics defined for coding and decoding purposes, mainly for block codes.
Obtaining binary perfect codes out of tilings
Gabriella Akemi Miyamoto, Marcelo Firer
A tiling of the -dimensional Hamming cube gives rise to a perfect code (according to a given metric) if the basic tile is a metric ball. We are concerned with metrics on the …
Metrics which turn tilings into binary perfect codes
Gabriella Akemi Miyamoto, Marcelo Firer
In this work, we consider tilings of the Hamming cube and look for metrics which turn the tilings into a perfect code. We consider the family of metrics which are determined by a w…
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…
A Distance Between Channels: the average error of mismatched channels
Rafael G. L. D'Oliveira, Marcelo Firer
Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a genera…