Parallel sentences in English and French, with mathematical expressions tokenized. The French sentences were extracted from course notes on error-correcting codes authored by Dr. Monica Nevins, University of Ottawa.

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Syntax-Directed Derivative Code (Part I: Tangent-Linear Code)

Uwe Naumann, Uwe Naumann · 2005

Abstract. This is the first instance in a series of papers on single-pass generation of various types of derivative code by syntax-directed translation. We consider the automatic generation of tangent-linear code by forward mode automatic differentiation implemented as the bottom-up propagation of synthesized attributes on the abstract syntax tree. A proof-of-concept implementation is presented based on a simple LALR(1) parser generated by the parser generator bison. The proposed technique can be generalized easily to provide a method for computing directional derivatives of mathematical vector functions that are implemented as computer programs in the context of computer algebra systems and compilers for scientific computing. The main advantage of the syntax-directed approach to automatic differentiation is its elegance in terms of the implementation. 1 Motivation and Summary of Results This paper presents a method for generating tangent-linear versions of numerical simulation programs 1 that implement vector functions F: IR n → IR m, y = F (x), x = (xk)k=1,...,n, y = (yl)l=1,...,m, (1) automatically by syntax-directed translation. Such tangent-linear programs ˙ F = F ˙ (x, ˙x) compute directional derivatives ˙y, that is, products of the Jacobian matrix F ′ = (f ′ l,k)l=1,...,m k=1,...,n ≡ � �l=1,...,m ∂yl ∈ IR ∂xk k=1,...,n m×n

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A Code for Linear Stability Analysis

Thorwald Herbert · ICASE/NASA LaRC series · 1990

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Appendix 5: Bayesian linear model code

Michel, Nicole L., Smith, Adam C., Clark, Robert G. et al. · DRYAD · 2015

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Composing Transformations to Optimize Linear Code

Thomas Noll, Stefan Rieger · Lecture notes in computer science · 2007

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Code transformations for variant linear quadtrees

Peimin Chen · 2002

Depth-first (DF) and breath-first (BF) linear quadtree representations have the advantages in the performance of image operations and the storage requirements respectively. In this paper, the general guidelines and algorithms for code transformation between BF and DF linear quadtrees are proposed. Thus, we can exploit the advantages of DF and BF representations without suffering their drawbacks. Here, one typical DF linear quadtree scheme (Gargantini, 1982), and two BF linear quadtree schemes with different styles, FBLQ (Chang et al., 1994) with variant length and CBLQ (Lin), with constant length, are selected to depict the guidelines and algorithms. Each algorithm has time complexity O(l), where l is the length of the transformed code. This complexity is much less than that of the BF or DF encoding process for the corresponding image, which is at least of the same order as the number of pixels in this image.

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OPTIMAL EXTENSION OF A LINEAR CODE.

Afrati, F, Papaspirou, V · DSpace - NTUA (National Technical University of Athens) · 1985

The authors attack the problem of optimally extending the dimension of a linear binary block code by increasing its length but retaining its minimum Hamming distance. After defining some decisive characteristics of a code affecting its extension capabilities and proving some preliminary results, the authors give a necessary and sufficient condition for a code to be optimally extended. This result can be readily used to decide the existence of a code from the existence of another shorter code of which the first can be an extension, and this can be also done in a recursive manner, ending up with the need to examine the properties of much shorter codes.

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Weighted decoding of linear block code

Fang, Juing, Ecole Nationale Superieure des Telecommunications (ENST), 75 - Paris (France) · OpenGrey (Institut de l'Information Scientifique et Technique) · 1986

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LINEAR CODE THROUGH POLYNOMIAL MODULO Z

MAKARIM ABDULWAHIDE · Journal of university of Anbar for pure science · 2012

A polynomial p(x)= a + a x + …+ a x is said to be a permutation polynomial over a finite ring R If P permute the elements of R . where R is the ring ( Z , + , ) . It is known that mutually orthogonal Latin of order n,where n is the element in Z generate A [ ] – error correcting code with n code words . And we found no a pair of polynomial defining a pair of orthogonal Latin square modulo Z where n = 2 generate a linear code.

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An optimal linear code over F11

Chimal Dzul, Henry, Díaz Vargas, Javier · Dialnet (Universidad de la Rioja) · 2009

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Burst distribution of a linear code

Bal Kishan Dass, Siri Krishan Wasan, Arthur L. Rubin · Journal of Combinatorial Theory Series A · 1983

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Translating Structured Commands Into Linear Code

Mark Saaltink · 1993

Introduction The final phase of the Verdi compiler translates a structured intermediate language into a sequence of instructions, jumps, conditional jumps, and (pseudo-)instructions that define labels. This transformation can be defined and proved correct in a quite general setting. To that end, we define that transformation in terms of a syntax that includes some unspecified set of &quot;primitive&quot; commands, and a semantics that is based on some unspecified semantic functions. 2 Parameterization We will assume a set Prim of primitive actions and a set Test of primitive tests. We further assume a semantic domain A of semantic actions. We suppose that v is a partial order on A that makes (A; v) a chain-complete parial order [1]. In particular, then, any monotonic function from A to A has a least fixed point. We assume the existence o

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On Syntax-Directed Tangent-linear Code

Naumann, Uwe, Gendler, Dmitrij, Varnik, Ebadollah · RWTH Publications (RWTH Aachen) · 2007

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Code multiplexing using linear block codes

A V Rabin, Steven Rabin, Arseniy Zyulkov · EPJ Web of Conferences · 2025

This paper explores the application of code multiplexing using linear block codes in communication systems. Through a comprehensive analysis of contemporary literature on switching methods and signal modeling, the study investigates the principles of code channel division switching. The research proposes novel approaches for synthesizing orthogonal encoding and decoding matrices, enabling efficient channel division through simplified schemes. The study focuses on the implementation of code division multiplexing using block codes, highlighting its potential for enhancing communication efficiency. Additionally, the paper discusses the dual benefit of this approach, noting its capacity for simultaneous error correction during the channel division process. This feature underscores the method's potential for improving both the reliability and efficiency of data transmission in various communication systems

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