Lexicodes Research Articles

The Active Learner’s Construction-Combinatory Thesaurus: user-driven principles of compiling (a cognitive linguistic approach)

This article discusses the design of a new type of dictionaries, the Active Learner’s Construction-Combinatory Thesaurus (ALCCT) intended for adult learners of the second (foreign) language. The ALCCT is an ideographic dictionary where phrases, understood as instantiations of constructions, are arranged in accordance with the cognitive ontology of a particular conceptual thematic field. As such, the ALCCT is a project compatible with cognitive lexicography, a contemporary branch of dictionary-making that adopts the findings of cognitive science, cognitive linguistics in particular. The article proposes a cognitive profile of the dictionary’s target user, and makes it a departure point in elaborating the principles of compiling the ALCCT. They are defined as the principles of data selection, arrangement, and application. Data selection regards their thematic and formal coherence, their authenticity, and their prominence, or frequency. Data arrangement implies their relational coherence, and their elaboration. Relational coherence is realized through the lexicographic code, or the dictionary’s overall design that develops at three hierarchical levels: those of macrostructure (a conceptual ontology of the theme), mediostructure (the key words evolving into phrasal sets), and microstructure (description of phrasal lemmas). Elaboration of the data is provided via the overarching structure mapped onto the three hierarchical structures of the lexicographic code, and concerned with etymological, cultural, grammatical, and phraseological (metaphorical) extensions. Data application reaches out to the communicative situations in which the ALCCT’s resources can be used.

Todas por uma: as línguas na língua de Guimarães Rosa

Abstract – The literary language of Guimaraes Rosa appears to reproduce the popular language of Minas Gerais, however within it we can also find cultism, quotes, archaisms, neologisms, calques, linguistic loans, in a mix that seems completely natural. Drawing upon Nilce Sant’Anna Martins’ Lexico de Gumaraes Rosa (Sao Paulo, 2001), I will observe a selection of neologisms devised by Rosa that are formed by hexogen elements from foreign languages (old and modern). Furthermore, I will attempt to demonstrate how this phenomenon could stem from the influence that critical reflections on language deriving from linguistic theory and characterizing the hermeneutical practices of the 20th century (from Modernism to neo-vanguards) had on Guimaraes.

A selection of divisible lexicographic codes

This paper presents a selection of lexicographic codes over a prime field F p, codes constructed so as to be linear and to have a prescribed minimum distance and divisor. The development of the code when the minimum distance is 3p and the divisor is p leads to questions involving the distribution of quadratic residues and non-residues modulo p. In the course of events, the Hall plane H (p) emerges. This paper is dedicated to Vera Pless on the occasion of her retirement. She was in the audience when I presented a sketchy version of the material at a conference at Lehigh University many years ago. In my enthusiasm, I promised her a paper on the subject – and here it is, at last!

Self-dual codes over the Kleinian four group

We introduce self-dual codes over the Kleinian four group K=Z2×Z2 for a natural quadratic form on Kn and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail.

Self-dual codes over the Kleinian four group

We introduce self-dual codes over the Kleinian four group K=Z 2×Z 2 for a natural quadratic form on K n and develop the theory. Topics studied are: weight enumerators, mass formulas, classification up to length 8, neighbourhood graphs, extremal codes, shadows, generalized t-designs, lexicographic codes, the Hexacode and its odd and shorter cousin, automorphism groups, marked codes. Kleinian codes form a new and natural fourth step in a series of analogies between binary codes, lattices and vertex operator algebras. This analogy will be emphasized and explained in detail.

Designing lexicographic codes with a given trellis complexity

We generalize constructions of lexicographic codes to produce locally optimal codes with a desired trellis decoding complexity. These constructions are efficient for high-rate codes and provide a means for automated code design. As a byproduct, we improve known bounds on the parameters of lexicodes.

A decoding scheme for the 4‐ary lexicodes with D = 3

We introduce the algorithms for basis and decoding of quaternary lexicographic codes with minimum distance d = 3 for an arbitrary length n.

New constructions for covering designs

AbstractA(v, k, t) covering design, or covering, is a family of k‐subnets, called blocks, chosen from a v‐set, such that each t‐subnet is contained in at least one of the blocks. The number of blocks is the covering's size, and the minimum size of such a covering is denoted by C(v,k,t). This paper gives three new methods for constructing good coverings; a greedy algorithm similar to Conway and Sloane's algorithm for lexicographic codes [6], and two methods that synthesize new coverings from preexisting ones. Using these new methods, together with results in the literature, we build tables of upper bounds on C(v,k,t) for v ⩽ 32, k ⩽ 16, and t ⩽ 8. © 1995 John Wiley & Sons, Inc.

Minimal distance lexicographic codes over an infinite alphabet

The author investigates the properties of minimal distance lexicographic codes, or lexicode, over the ordered infinite alphabet N=(0,1,2...). The author presents a method for computing the basis of such a code. It is shown that any lexicographic code S with minimal distance d has a unique basis where each basis vector is a one followed by a string of zeros, followed by d-1 nonzero digits a/sub ij/. Furthermore, the matrix A=(a/sub ij/) has no singular minors over the nim-field. The dual code when S has finite length is also computed. The author develops a systematic approach to determine which words belong to these lexicodes. >

Integral lexicographic codes

Lexicographic codes are mysterious things. Their definition is very simple-for a suitable notion of nearness one simply enumerates codewords in lexicographic order, always taking the next codeword to be the earliest word that is not prohibitively near to any earlier codeword. One would expect the resulting codes to have no very interesting properties, but in fact there is a quite remarkable amount of structure that is by no means apparent at first sight. The main aim of [2] was to show how lexicographic codes are essentially the same as certain games, and the main theorem of that paper, which we shall call the Lexicode Theorem, was there deduced using the known theory of impartial games. The plan of this paper is rather different. Here we first take a weak form of the Lexicode Theorem as an axiom. Although its statement below seems very simple and natural, we shall show how strange it really is by exploring its surprising arithmetical consequences. Having thus whetted the reader’s appetite, we shall then provide more solid fare by proving the Lexicode Theorem in a new and very easy way. Actually, the theorem splits naturally into two parts, the Additive and Multiplicative theorems, and the new proof establishes much stronger forms of these than the originals in [2]. We show that the new forms are best possible in at least one sense-any code that satisfies the conclusion of either theorem can be defined in at least one way that satisfies the hypotheses of that theorem, although it might also have more interesting definitions perhaps not covered by that theorem. We shall also give some interesting examples of particular integral lexicodes, and explain some tricks that are useful in computing them. In particular we shall incorporate (with his permission) some recent results of David Herscovici on minimum distance lexicographic codes and describe his work on precluded distance lexicographic codes. Finally, and for amusement only, we return to the associated arithmetic to consider some elementary diophantine equations and pose some problems.

Lexicographic codes: Error-correcting codes from game theory

Lexicographic codes, or lexicodes, are defined by various versions of the greedy algorithm. The theory of these codes is closely related to the theory of certain impartial games, which leads to a number of surprising properties. For example, lexicodes over an alphabet of size B=2^{a} are closed under addition, while if B = 2^{2^{a}} the lexicodes are closed under multiplication by scalars, where addition and multiplication are in the nim sense explained in the text. Hamming codes and the binary Golay codes are lexieodes. Remarkably simple constructions are given for the Steiner systems S(5,6,12) and S(5,8,24) . Several record-breaking constant weight codes are also constructed.

The Mathematical Association of America

s and Biographies of Speakers The Mysterious Arithmetic of Lexicographic Codes John H. Conway, Princeton University The Mathematical Association of America Integral lexicographic codes are very simply defined (by a “greedy algorithm”), but have strange arithmetical properties that are hidden in a theorem I call “The Lexicode Theorem.” I'll tell you what the theorem says, and together we'll puzzle out what (if anything) it means. New Jersey Section Spring Meeting Rutgers University New Brunswick, NJ Saturday, March 27, 2004 2 John H. Conway is John von Neumann Distinguished Professor of Mathematics at Princeton University, NJ. Born in Liverpool, England, he received his education at the University of Cambridge and then taught at Cambridge for many years before joining the Princeton faculty in 1986. Conway is the author or co-author of at least ten books, and of many expository articles which have had substantial impact not just on research mathematicians but on mathematical amateurs as well. Conway has a rare gift for naming mathematical objects, and for inventing useful mathematical notations. He is widely known for his discovery of surreal numbers, the Conway group, and for inventing the Game of Life. Conway is a Fellow of the Royal Society, a Member of the American Association for the Advancement of Science, and recipient of the Berwick Prize of the London Mathematical Society (1971), Polya Prize of the London Mathematical Society (1987), Frederic Esser Nemmers Prize (1999), Leroy P. Steele Prize of the American Mathematical Society (2000), and Joseph Priestley Award (2001). He received an honorary doctorate from the University of Liverpool on July 4, 2001. Designing the Pre-service Teacher Curriculum to Better Meet the Needs of Our Future Teachers Mercedes McGowen, William Rainey Harper College David Ausubel claimed that “the single most important factor influencing learning is what the learner already knows. Ascertain this and teach him accordingly.” How do we determine what a student already knows and then use the evidence of learning that we collect to improve our teaching and student learning? What classroom experiences foster the development of mathematical thinking—pattern recognition, generalization, abstraction, problem solving, careful analysis, rigorous argument and flexible thinking? Designing a curriculum that builds on students’ prior knowledge to develop these skills effectively and at appropriate levels for all students is one of the biggest and most important challenges we face. To address these questions, we will analyze some mathematical tasks that illustrate how mathematical