相关论文: On a linear code from a configuration of affine li…

In this work, we modify the decoding algorithm for subspace codes by Koetter and Kschischang to get a decoding algorithm for (generalized) twisted Gabidulin codes. The decoding algorithm we present applies to cases where the code is linear…

Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…

Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

In exchange for large quantities of data and processing power, deep neural networks have yielded models that provide state of the art predication capabilities in many fields. However, a lack of strong guarantees on their behaviour have…

In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their…

Verifying specifications for large-scale modern engineering systems can be a time-consuming task, as most formal verification methods are limited to systems of modest size. Recently, contract-based design and verification has been proposed…

In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq (q = 2^m) using Pascal…

An elementary proof of the attainability of random coding exponent with linear codes for additive channels is presented. The result and proof are from Hamada (Proc. ITW, Chendu, China, 2006), and the present material explains the proof in…

For affine plane curves defined over the rationals of genus at least two, we show that a decision algorithm for the existence of solutions also yields a search algorithm for all solutions.

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…

Optical quasar spectra can be used to trace variations of the fine-structure constant alpha. Controversial results that have been published in last years suggest that in addition to to wavelength calibration problems systematic errors might…

This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise…

Sparse random linear network coding (SRLNC) is an attractive technique proposed in the literature to reduce the decoding complexity of random linear network coding. Recognizing the fact that the existing SRLNC schemes are not efficient in…

In this paper, we tie together two well studied topics related to finite Desarguesian affine and projective planes. The first topic concerns directions determined by a set, or even a multiset, of points in an affine plane. The second topic…

We present a precise characterization of linear functional-repair storage codes in terms of {\em admissible states/}, with each state made up from a collection of vector spaces over some fixed finite field. To illustrate the usefulness of…

A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…

In this paper, we establish a lemma in algebraic coding theory that frequently appears in the encoding and decoding of, e.g., Reed-Solomon codes, algebraic geometry codes, and affine variety codes. Our lemma corresponds to the…

We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…