This paper improves the lower bound on the maximum size of trifferent codes using a locally sparse hypergraph and the Verstraete-Wilson theorem.

This paper introduces a structural theorem for the sparsifiability of real-valued codes, which generalizes both combinatorial and continuous notions of sparsification.

This paper introduces a new way to represent finite posets as subwords of finite words in categories, and characterizes the monic categories that admit this representation.

A new boosting algorithm that strong learns concept classes closed under O(log 1/γ)-XOR using O(log 1/ε) calls to a γ-advantage weak learner and additional samples, by connecting boosting with list-de…

This paper proves that the min-plus factorization rank and tropical rank of a binary linear code's conditional decoding matrix equal 2^s, where s is the classical state complexity of the minimal trell…

This paper introduces minimal additive codes over Fqh and establishes a one-to-one correspondence between minimal additive codes and additive strong blocking sets. It also compares this framework with…

The paper studies properties of parity based bit-counting complexity classes B|0|⊕P and B|1|⊕P, proves inclusions and closures, and shows they contain PH and are contained in CH.

This paper establishes a Coding Theorem in the context of symmetry groups and develops a connection between subgroups of a group and subsets of binary strings.

This paper characterizes acyclic hypergraphs according to whether they admit unique canonical join trees as root and provides a linear-time algorithm to construct them.

This paper studies the maximum size of an independent set in the discrete simplex graph and provides new bounds using translated smaller graphs and finite rational linear systems.

The paper constructs Schubert subspace codes with maximum possible size in certain extremal distance cases using two methods: direct-sum decomposition and field reduction.

This paper provides bounds on the difference between the annihilation number and independence number of a finite simple graph, and proves these bounds for various types of graphs.

This paper settles the complexity of three sketching problems in graphs and distributions.

This paper studies the triangle-densest-$k$-subgraph problem in an average-case model and proposes spectral and semidefinite algorithms for its recovery.

This paper proves that for any finite abelian group, there exists a spectral sparsifier for its Cayley graph with log(|G|) generators. This result improves upon previous work for constructing code spa…

This paper generalizes the connection between graph theory, association schemes, and coding theory to the space of tensors over a finite field, and derives the spectrum of the corresponding graph.

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…