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

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

The paper proves a stochastic comparison for Gaussian maxima, resolving the Weak Simplex Conjecture and proving the Simplex Mean Width Conjecture.

This paper develops a new decoding algorithm for Desarguesian spread codes to uniquely decode in the presence of insertions and deletions, even when the sum of their dimensions exceeds half the minimu…

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

This paper connects a generalized notion of tensor rank with multiplicative complexity, enabling control of arithmetic complexity in any constant degree of multilinearity and applications to fine-grai…

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 derives an explicit representation for the Euclidean dual of Hyperderivative Reed-Solomon codes and studies reverse self-dual HRS codes.

This paper presents a local computation algorithm to approximate the top eigenvector of a symmetric matrix with entries between -1 and 1, building on Swartworth and Woodruff's work.

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

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.

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…

This paper proposes the first constant-time decoding algorithm for Augmented Gabidulin (AG) codes, a variation of Gabidulin codes used in efficient rank-based cryptosystems.

The paper analyzes the security of the post-quantum signature scheme CROSS by showing that the underlying Restricted Syndrome Decoding problem can be reduced to both code-based and lattice-based probl…