15 citations · 34 across the 13 of their papers we have counts for
8 papers · 1 filter
Decreasing norm-trace codes
Cícero Carvalho, Hiram H. López, Gretchen L. Matthews
The decreasing norm-trace codes are evaluation codes defined by a set of monomials closed under divisibility and the rational points of the extended norm-trace curve. In particular…
A family of codes with variable locality and availability
Cícero Carvalho, Victor G. L. Neumann
In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position of a codeword may be recovered from the knowledge of the entries in the…
A family of codes with locality containing optimal codes
Bruno Andrade, Cícero Carvalho, Victor G. L. Neumann +1
Locally recoverable codes were introduced by Gopalan et al. in 2012, and in the same year Prakash et al. introduced the concept of codes with locality, which are a type of locally…
On the next-to-minimal weight of projective Reed-Muller codes
Cícero Carvalho, Victor G. L. Neumann
In this paper we present several values for the next-to-minimal weights of projective Reed-Muller codes. We work over with since in IEEE-IT 62(11) p. 6300…
The next-to-minimal weights of binary projective Reed-Muller codes
Cícero Carvalho, Victor G. L. Neumann
Projective Reed-Muller codes were introduced by Lachaud, in 1988 and their dimension and minimum distance were determined by Serre and Sørensen in 1991. In coding theory one is als…
On the second Hamming weight of some Reed-Muller type codes
Cicero Carvalho
We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. Thes…