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09/07/2023
LRCs: Duality, LP Bounds, and Field Size
We develop a duality theory of locally recoverable codes (LRCs) and appl...
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07/27/2023
Knot Theory and Error-Correcting Codes
This paper builds a novel bridge between algebraic coding theory and mat...
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07/25/2023
Eigenvalue Bounds for Sum-Rank-Metric Codes
We consider the problem of deriving upper bounds on the parameters of su...
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07/17/2023
Multishot Adversarial Network Decoding
We investigate adversarial network coding and decoding focusing on the m...
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03/07/2023
The Service Rate Region Polytope
We investigate the properties of a family of polytopes that naturally ar...
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12/15/2022
Duality and LP Bounds for Codes with Locality
We initiate the study of the duality theory of locally recoverable codes...
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12/15/2022
ℓ-Complementary Subspaces and Codes in Finite Bilinear Spaces
We consider (symmetric, non-degenerate) bilinear spaces over a finite fi...
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12/14/2022
Network Coding: An Optimization Approach
We consider the problem of computing the capacity of a coded, multicast ...
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09/12/2022
Rook Theory of the Etzion-Silberstein Conjecture
In 2009, Etzion and Siberstein proposed a conjecture on the largest dime...
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08/22/2022
Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces
We investigate the asymptotic density of error-correcting codes with goo...
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06/18/2022
Rank-Metric Lattices
We introduce the class of rank-metric geometric lattices and initiate th...
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05/29/2022
Network Decoding
We consider the problem of error control in a coded, multicast network, ...
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01/19/2022
Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery
We are concerned with linear redundancy storage schemes regarding their ...
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01/18/2022
Rank-Metric Codes, Semifields, and the Average Critical Problem
We investigate two fundamental questions intersecting coding theory and ...
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01/15/2022
Generalized weights of codes over rings and invariants of monomial ideals
We develop an algebraic theory of supports for R-linear codes of fixed l...
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07/05/2021
The Curious Case of the Diamond Network
This work considers the one-shot capacity of communication networks subj...
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06/23/2021
Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric
This work investigates the structure of rank-metric codes in connection ...
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05/10/2021
The Typical Non-Linear Code over Large Alphabets
We consider the problem of describing the typical (possibly) non-linear ...
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11/16/2020
Parameters of Combinatorial Neural Codes
Motivated by recent developments in the mathematical theory of neural co...
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11/05/2020
Common Complements of Linear Subspaces and the Sparseness of MRD Codes
We consider the problem of estimating the number of common complements o...
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10/30/2020
Three Combinatorial Perspectives on Minimal Codes
We develop three approaches of combinatorial flavour to study the struct...
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10/06/2020
Fundamental Properties of Sum-Rank Metric Codes
This paper investigates the theory of sum-rank metric codes for which th...
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09/23/2019
Whitney Numbers of Combinatorial Geometries and Higher-Weight Dowling Lattices
We study the Whitney numbers of the first kind of combinatorial geometri...
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04/10/2019
Tensor Representation of Rank-Metric Codes
We present the theory of rank-metric codes with respect to the 3-tensors...
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11/03/2018
Partitions of Matrix Spaces With an Application to q-Rook Polynomials
We study the row-space partition and the pivot partition on the matrix s...
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06/01/2018
An Assmus-Mattson Theorem for Rank Metric Codes
A t-(n,d,λ) design over F_q, or a subspace design, is a collection of d...
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05/05/2018
Partition-Balanced Families of Codes and Asymptotic Enumeration in Coding Theory
We introduce the class of partition-balanced families of codes, and show...
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03/28/2018