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 introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.

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

This paper identifies new, algebraically weak classes of instances for the Linear Equivalence Problem (LEP) by generalizing techniques from the Permutation Equivalence Problem (PEP) using power codes…

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 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 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…

This paper shows that any boolean matrix with bounded factorization norm can be expressed as a signed sum of blow-up identity matrices, and this result has applications to matrix sequences and complex…

This paper introduces a robust OR polynomial framework to derive certificates for positive semidefinite matrices across OR constraints, and applies it to acute-free families and multicolor Ramsey numb…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

The paper analyzes subcodes of lambda-Gabidulin codes to construct highly efficient McEliece-like and Niederreiter-like cryptosystems, demonstrating that random subcodes of classical Gabidulin codes y…

The paper systematically investigates the conditions under which linear layers in AES-like ciphers avoid related-differential structures, proving that the MDS property is necessary and identifying spe…

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 proves that random linear codes have nearly optimal discrepancy properties in various regimes, extending classical results and enabling new applications.

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 proves that the maximum of up to 10 real numbers can be exactly represented by a ReLU network with two hidden layers, and shows that the same depth bound holds for all continuous piecewise-…