12 papers · 1 filter
A Matroidal Framework for Random Access in Linear Codes
Daniella Bar-Lev, Hiram H. López, Gretchen L. Matthews +1
We study random access in linear codes when codeword symbols are sampled independently and uniformly with replacement. A code is recovery balanced if the expected number of samples…
Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
Delio Jaramillo-Velez, Alessandro Neri, Adway Patra +2
CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a tr…
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
The Length of Functional Batch and PIR Codes
Altan B. Kilic, Alberto Ravagnani, Flavio Salizzoni
We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover,…
Latroids and code invariants
Elisa Gorla, Flavio Salizzoni
Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. The origina…
A geometric invariant of linear rank-metric codes
Valentina Astore, Martino Borello, Marco Calderini +1
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscro…
Integer sequences that are generalized weights of a linear code
Elisa Gorla, Elisa Lorenzo García, Umberto Martínez-Peñas +1
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally…
MacWilliams' Extension Theorem for rank-metric codes
Elisa Gorla, Flavio Salizzoni
The MacWilliams' Extension Theorem is a classical result by Florence Jessie MacWilliams. It shows that every linear isometry between linear block-codes endowed with the Hamming dis…
Sum-rank metric codes
Elisa Gorla, Umberto Martínez-Peñas, Flavio Salizzoni
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network co…
Generalized column distances
Elisa Gorla, Flavio Salizzoni
We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column…
Generalized weights of convolutional codes
Elisa Gorla, Flavio Salizzoni
In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Ha…
Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric
Eduardo Camps Moreno, Elisa Gorla, Cristina Landolina +3
Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural ge…