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Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial…
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evaluation step. We improve the bound on the number of errors that…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Linear codes and $t$-designs are interactive with each other. It is well known that some $t$-designs have been constructed by using certain linear codes in recent years. However, only a small number of infinite families of the extended…
Given a commutative ring $R$ with identity, a matrix $A\in M_{s\times l}(R)$, and $R$-linear codes $\mathcal{C}_1, \dots, \mathcal{C}_s$ of the same length, this article considers the hull of the matrix-product codes $[\mathcal{C}_1 \dots…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
One of the most important and challenging problems in coding theory is to determine the optimal values of the parameters of a linear code and to explicitly construct codes with optimal parameters, or as close to the optimal values as…
Precoded polar product codes are proposed, where selected component codes enable successive cancellation list decoding to generate bit-wise soft messages efficiently for iterative decoding while targeting optimized distance spectrum as…
LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality…
Two new constructions of linear code pairs $C_2 \subset C_1$ are given for which the codimension and the relative minimum distances $M_1(C_1,C_2)$, $M_1(C_2^\perp,C_1^\perp)$ are good. By this we mean that for any two out of the three…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…