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

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…

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

The paper derives an explicit representation for the Euclidean dual of Hyperderivative Reed-Solomon codes and studies reverse self-dual HRS 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 introduces and studies the block tensor rank of sum-rank metric codes, showing its additive decomposition and deriving lower bounds.

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…

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 polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

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 presents a new nondeterministic finite automaton (NFA) for recognizing repetition-free words over a given alphabet, improving on the previous construction.

This paper introduces a symbolic diagnostic approach for investigating obstruction structures in the Collatz conjecture using finite exponent codes of the accelerated map.

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…