Related papers: On the Minimum Length of Functional Batch Codes wi…
A minimal code is a linear code where the only instance that a codeword has its support contained in the support of another codeword is when the codewords are scalar multiples of each other. Ashikhmin and Barg gave a sufficient condition…
In contrast to the network coding problem wherein the sinks in a network demand subsets of the source messages, in a network computation problem the sinks demand functions of the source messages. Similarly, in the functional index coding…
Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
Coded caching is a technique that leverages locally cached contents at the end users to reduce the network's peak-time communication load. Coded caching has been shown to achieve significant performance gains with a centralized placement…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
Rateless/fountain codes are designed so that all input symbols can be recovered from a slightly larger number of coded symbols, with high probability using an iterative decoder. In this paper we investigate the number of input symbols that…
Consider the case where a programmer has written some part of a program, but has left part of the program (such as a method or a function body) incomplete. The goal is to use the context surrounding the missing code to automatically 'figure…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…
Coded distributed batch computation distributes a computation task, such as matrix multiplication, $N$-linear computation, or multivariate polynomial evaluation, across $S$ servers through a coding scheme, such that the response from any…
This work introduces (1) a technique that allows large language models (LLMs) to leverage user-provided code when solving programming tasks and (2) a method to iteratively generate modular sub-functions that can aid future code generation…
Batched sparse (BATS) codes were proposed as a reliable communication solution for networks with packet loss. In the finite-length regime, the error probability of BATS codes under belief propagation (BP) decoding has been studied in the…
An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…
Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…
This work investigates a system where each user aims to retrieve a scalar linear function of the files of a library, which are Maximum Distance Separable coded and stored at multiple distributed servers. The system needs to guarantee robust…
Batch codes, introduced by Ishai, Kushilevitz, Ostrovsky and Sahai, represent the distributed storage of an $n$-element data set on $m$ servers in such a way that any batch of $k$ data items can be retrieved by reading at most one (or more…
We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which $n$ files are stored on $m$ servers so that every set of $n-r$ servers allows a client to retrieve at most $k$ distinct files by downloading at most $t$…
Distributed linearly separable computation, where a user asks some distributed servers to compute a linearly separable function, was recently formulated by the same authors and aims to alleviate the bottlenecks of stragglers and…
Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally…