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Nathan Lindzey (University of Memphis)5/18/26, 11:00 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
A family of permutations $\mathcal{F} \subseteq S_n$ is even-cycle-intersecting if $\sigma \pi^{-1}$ has an even cycle for all $\sigma,\pi \in \mathcal{F}$. We show that if $\mathcal{F} \subseteq S_n$ is an even-cycle-intersecting family of permutations, then $|\mathcal{F}| \leq 2^{n-1}$, and that equality holds when $n$ is a power of 2 and $\mathcal{F}$ is a double-translate of a Sylow...
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Matteo Bertuzzo (Eindhoven University of Technology)5/18/26, 11:25 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
The injection metric measures the distance between two subspaces and naturally arises in the context of subspace coding, when the codewords potentially have different dimensions. In this talk, we consider a graph associated with the injection metric and examine how its structure determines the existence of good codes for subspace coding.
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Michael Tait (Villanova University)5/18/26, 11:50 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
We discuss the use of graph theory methods to attack coding theory problems.
This is joint work with Aida Abiad and Harper Reijnders.
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Prof. Ken Duffy (Northeastern University)5/18/26, 2:00 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
The study of error correcting codes has two important facets: code construction and decoder design. Many graph-based code constructions have been established to have desirable theoretical properties, but, heretofore, have not been practically decodable. In this talk, we explain recent developments in code-agnostic decoders, including soft-input soft-output variants, that offer a way forward in...
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Shuxing Li (University of Delaware)5/18/26, 2:25 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Determining the minimum Hamming distance of an error-correcting code $\mathcal{C}$ has long stood as a fundamental challenge in coding theory. In this talk, we turn our attention to an even more ambitious problem: determining the full Hamming weight distribution of $\mathcal{C}$. This means counting the number of codewords in $\mathcal{C}$ of each possible Hamming weight—an essential but...
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Dr Kathryn Haymaker (Villanova University)5/18/26, 2:50 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
In this talk, we present a family of algebraically constructed hierarchical quasi-cyclic codes. These codes are built from Reed-Solomon and polynomial evaluation codes using a construction of superimposed codes by Kautz and Singleton. Using a novel ordering of the codewords and evaluation points, we show both the number of levels in the hierarchy and the index of these $q$-ary-derived codes...
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Rafael D'Oliveira (Clemson University)5/19/26, 11:00 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Matrix multiplication is, oftentimes, the most expensive computational task in an algorithm. It is the computational bottleneck for training many of the now well-celebrated learning algorithms, for example. To speed up the algorithm, the data can be distributed on many machines to perform the computations in parallel. This sharing of the data, however, raises security concerns when the data is...
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Dr Kirsten Morris (Virginia Tech)5/19/26, 11:25 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Dyadic matrices are a subclass of matrices known as reproducible matrices, where the entries of the matrix are completely determined by their first row. Quasi-dyadic matrices are block matrices with dyadic matrices in the blocks.
There has been extensive work analyzing quasi-cyclic codes, codes defined by quasi-cyclic parity check matrices, but less is known about codes arising from dyadic...
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Felice Manganiello (Clemson University)5/19/26, 11:50 AMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a finite field. In this context, we establish an outer bound for the achievable rate region and provide examples of networks where the bound is sharp. We...
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Valentino Smaldore (Università degli Studi di Padova)5/19/26, 2:00 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
Let $\mathcal{C} = \{c_0, c_1, \ldots, c_{q^k}\} \subseteq \mathbb{F}_q^n$ be a $[n,k]_q$-linear code endowed with the Hamming metric. That is, $\mathcal{C}$ is a $k$-subspace of $\mathbb{F}_q^n$. Let $M_{\mathcal{C}}\in\mathbb{R}^{q^k\times q^k}$ be the distance matrix of the code defined as $(M_\mathcal{C})_{i,j} := d_H(c_i, c_j)=|\{i\colon x_i\neq y_i\}|$. We analyze the spectrum of...
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Pedro Paredes (Princeton University)5/19/26, 2:25 PMWhere Algebraic Coding Theory and Graph Theory MeetMinisymposium Talk
This talk explores the interplay between coding theory and expander graphs. We will discuss key developments in the design of expander-based codes, including recent advancements that lead to locally testable codes and efficient quantum codes. This includes a review of work dedicated to designing vertex expanders and unique-neighbor expanders, focusing on the specific properties that make them...
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