pinecone/core-2020-05-10-deduplication huggingface dataset:
Error-Correcting Codes from Higher-Dimensional Varieties

AbstractIn this paper we use intersection theory to develop methods for obtaining lower bounds on the parameters of algebraic geometric error-correcting codes constructed from varieties of arbitrary dimension. The methods are sufficiently general to encompass many of the codes previously constructed from higher-dimensional varieties, as well as those coming from curves. And still, the bounds obtained are usually as good as the ones previously known (at least of the same order of magnitude with respect to the size of the ground field). Several examples coming from Deligne–Lusztig varieties, complete intersections of Hermitian hyper-surfaces, and from ruled surfaces (or more generally, projective bundles over a curve) are given
Recurrent Methods for Constructing Irreducible Polynomials over GF(2s)

AbstractThe paper is devoted to some results concerning the constructive theory of the synthesis of irreducible polynomials over Galois fields GF(q), q=2s. New methods for the construction of irreducible polynomials of higher degree over GF(q) from a given one are worked out. The complexity of calculations does not exceed O(n3) single operations, where n denotes the degree of the given irreducible polynomial. Furthermore, a recurrent method for constructing irreducible (including self-reciprocal) polynomials over finite fields of even characteristic is proposed
Partition, Construction, and Enumeration of M–P Invertible Matrices over Finite Fields

AbstractA necessary and sufficient condition for an m×n matrix A over Fq having a Moor–Penrose generalized inverse (M–P inverse for short) was given in (C. K. Wu and E. Dawson, 1998, Finite Fields Appl. 4, 307–315). In the present paper further necessary and sufficient conditions are obtained, which make clear the set of m×n matrices over Fq having an M–P inverse and reduce the problem of constructing M–P invertible matrices to that of constructing subspaces of certain type with respect to some classical groups. Moreover, an explicit formula for the M–P inverse of a matrix which is M–P invertible is also given. Based on this reduction, both the construction problem and the enumeration problem are solved by borrowing results in geometry of classical groups over finite fields (Z. X. Wan, 1993, “Geometry of Classical Groups over Finite Fields”, Studentlitteratur, Chatwell Bratt)
Counting Functions and Expected Values for the k-Error Linear Complexity

AbstractIn cryptology, complexity measures for sequences of elements of a finite field, such as the linear complexity, play an important role. Cryptographically strong sequences or finite strings must not only have a large linear complexity, but also the change of a few terms must not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity Ln,k(S) of a string S with terms in a finite field Fq and length n. In this article, bounds for the number of strings S of length n with k-error linear complexity Ln,k(S)=c or Ln,k(S)≤c for a given c are established. Under certain conditions on n, k, and c, exact formulas are also determined. On the basis of these results we derive bounds for the expected value of Ln,k(S) for random strings S of length n
Perfect Codes and Balanced Generalized Weighing Matrices, II

AbstractIn a previous paper, the authors proved that any set of representatives of the distinct 1-dimensional subspaces in the dual code of the unique linear perfect single-error-correcting code of length (qd−1)/(q−1) over GF(q) is a balanced generalized weighing matrix over the multiplicative group of GF(q). Moreover, this matrix was characterized as the unique (up to monomial equivalence) weighing matrix for the given parameters with minimum q-rank. We now relate these matrices to m-sequences (that is, linear shift register sequences of maximal period) by giving an explicit description in terms of the trace function; in this way, we show that a simple modification of our method can be used to obtain the matrices which are given by the “classical,” more involved construction going back to Berman. Moreover, further modifications of our matrices actually yield a wealth of monomially inequivalent examples, namely matrices for many different q-ranks
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions

AbstractWe use a general property of Fourier transform to obtain direct proofs of recent divisibility results on the Walsh transform of correlation immune and resilient functions. Improved upper bounds on the nonlinearity of these functions are obtained from the divisibility results. We deduce further information on correlation immune and resilient functions. In particular, we obtain a necessary condition on the algebraic normal form of correlation immune functions attaining the maximum possible nonlinearity
Type II Codes over F4

AbstractThe natural analogues of Lee weight and the Gray map over F4 are introduced. Self-dual codes for the Euclidean scalar product with Lee weights multiple of 4 are called Type II. They produce Type II binary codes by the Gray map. All extended Q-codes of length a multiple of 4 are Type II. This includes quadratic residue codes attached to a prime p≡3 (mod8), certain double circulant codes, and some affine invariant codes. A general mass formula is derived, a new upper bound for Euclidean self-dual codes over F4 is given, and the first extremal self-dual [92, 46, 16] binary code is built
Incomplete Character Sums and Polynomial Interpolation of the Discrete Logarithm

AbstractIn the first part of the paper, certain incomplete character sums over a finite field Fpr are considered which in the case of finite prime fields Fp are of the form ∑A+N−1n=Aχ(g(n))ψ(f(n)), where A and N are integers with 1≤N<p, g and f are polynomials over Fp, and χ denotes a multiplicative and ψ an additive character of Fp. Excluding trivial cases, it is shown that the above sums are at most of the order of magnitude N1/2pr/4. Recently, Shparlinski showed that a polynomial f over the integers which coincides with the discrete logarithm of the finite prime field Fp for N consecutive elements of Fp must have a degree at least of the order of magnitude Np−1/2. In this paper this result is extended to arbitrary Fpr. The proof is based on the above new bound for incomplete hybrid character sums
Finite Field Towers: Iterated Presentation and Complexity of Arithmetic

AbstractFinite field towers GF(qP) are considered, where P=pn11Pn22··· pntt and all primes pi are distinct factors of (q – 1). Under this condition irreducible binomials of the form xP – c can be used for recursive extension of finite fields. We give description of an infinite sequence of irreducible binomials, new effective algorithms for fast multiplication and inversion in the tower, and finite and asymptotic estimates of arithmetic complexity. It is important that the achievable asymptotic estimate of the complexity has the form O(logQlogξlogQ), Q=qP, where log2γ≥ξ≥1 and γ is the minimal factor of q–1
Highly Symmetric Expanders

AbstractExpander graphs are relevant to theoretical computer science in addition to the construction of high-performance switching networks. In communication network applications, a high degree of symmetry in the underlying topology is often advantageous, as it may reduce the complexity of designing and analyzing switching and routing algorithms. We give explicit constructions of expander graphs that are highly symmetric. In particular, we construct infinite families of Ramanujan graphs with large guarantees on the orders of their automorphism groups. Although nonlinear, our expander graphs are within a constant factor of the size of the smallest graphs exhibiting the same expansion properties. This work generalizes and extends in several directions a previous explicit construction of expander graphs based on finite projective spaces due to Alon
On Metric Diophantine Approximation in the Field of Formal Laurent Series

AbstractB. deMathan (1970, Bull. Soc. Math. France Supl. Mem.21) proved that Khintchine’s Theorem has an analogue in the field of formal Laurent series. First, we show that in case of only one inequality this result can also be obtained by continued fraction theory. Then, we are interested in the number of solutions and show under special assumptions that one gets a central limit theorem, a law of iterated logarithm and an asymptotic formula. This is an analogue of a result due to W. J. LeVeque (1958, Trans. Amer. Math. Soc.87, 237–260). The proof is based on probabilistic results for formal Laurent series due to H. Niederreiter (1988, in Lecture Notes in Computer Science, Vol. 330, pp. 191–209, Springer-Verlag, New York/Berlin)
On the Structure of Order Domains

AbstractThe notion of an order domain is generalized. The behaviour of an order domain by taking a subalgebra, the extension of scalars, and the tensor product is studied. The relation of an order domain with valuation theory, Gröbner algebras, and graded structures is given. The theory of Gröbner bases for order domains is developed and used to show that the factor ring theorem and its converse, the presentation theorem, hold. The dimension of an order domain is related to the rank of its value semigroup
MDS Self-Dual Codes over Large Prime Fields

AbstractCombinatorial designs have been used widely in the construction of self-dual codes. Recently a new method of constructing self-dual codes was established using orthogonal designs. This method has led to the construction of many new self-dual codes over small finite fields and rings. In this paper, we generalize this method by using generalized orthogonal designs, and we give another new method that creates and solves Diophantine equations over GF(p) in order to find suitable generator matrices for self-dual codes. We show that under the necessary conditions these methods can be applied as well to small and large fields. We apply these two methods to study self-dual codes over GF(31) and GF(37). Using these methods we obtain some new maximum distance separable self-dual codes of small orders
The Number of Permutation Polynomials of a Given Degree Over a Finite Field

AbstractWe relate the number of permutation polynomials in Fq[x] of degree d≤q−2 to the solutions (x1,x2,…,xq) of a system of linear equations over Fq, with the added restriction that xi≠0 and xi≠xj whenever i≠j. Using this we find an expression for the number of permutation polynomials of degree p−2 in Fp[x] in terms of the permanent of a Vandermonde matrix whose entries are the primitive pth roots of unity. This leads to nontrivial bounds for the number of such permutation polynomials. We provide numerical examples to illustrate our method and indicate how our results can be generalised to polynomials of other degrees
On the Average Distribution of Inversive Pseudorandom Numbers

AbstractThe inversive congruential method is an attractive alternative to the classical linear congruential method for pseudorandom number generation. The authors have recently introduced a new method for obtaining nontrivial upper bounds on the multidimensional discrepancy of inversive congruential pseudorandom numbers in parts of the period. This method has also been used to study the multidimensional distribution of several other similar families of pseudorandom numbers. Here we apply this method to show that, “on average” over all initial values, much stronger results than those known for “individual” sequences can be obtained
Enumerating Permutation Polynomials I: Permutations with Non-Maximal Degree

AbstractLet C be a conjugation class of permutations of a finite field Fq. We consider the function NC(q) defined as the number of permutations in C for which the associated permutation polynomial has degree <q−2. In 1969, Wells proved a formula for N[3](q) where [k] denotes the conjugation class of k-cycles. We will prove formulas for N[k](q) where k=4,5,6 and for the classes of permutations of type [2 2],[3 2],[4 2],[3 3] and [2 2 2]. Finally in the case q=2n, we will prove a formula for the classes of permutations which are product of 2-cycles
Compressing Mappings on Primitive Sequences over Z/(2e) and Its Galois Extension

AbstractLet f(x) be a strongly primitive polynomial of degree n over Z/(2e), η(x0,x1,…,xe−2) a Boolean function of e−1 variables and ϕ(x0,x1,…,xe−1)=xe−1+η(x0,x1,…,xe−2)G (f(x),Z/(2e)) denotes the set of all sequences over Z/(2e) generated by f(x), F2∞ the set of all sequences over the binary field F2, then the compressing mapping Φ : G(f(x),Z/(2e))→F2∞,a=a0+a12+···+ae−12e−1↦ϕ(a0,a1,…,ae−1) mod 2 is injective, that is, for a,b∈G(f(x),Z/(2e)), a=b if and only if Φ(a)=Φ(b), i.e., ϕ(a0,…,ae−1)=ϕ(b0,…,be−1) mod 2. In the second part of the paper, we generalize the above result over the Galois rings
Coalition-proof equilibrium

We characterize the agreements that the players of a noncooperative game may
reach when they can communicate prior to play, but they cannot reach binding
agreements: A coalition-proo[ equilibrium is a correlated strategy from which no
coalition has an improving and self-enforcing deviation. We show that any correlated strategy whose support is contained in the set of actions that survive the iterated elimination of strictly dominated strategies and weakly Pareto dominates every other correlated strategy whose support is contained in that set, is a
coalition-proof equilibrium. Consequently, the unique equilibrium of a dominance
solvable game is coalition-proof.Publicad
An experimental study of communication and coordination in noncooperative games

This paper reports the results of an experiment designed to test the usefulness of alternative solution concepts to explain players' behavior in noncooperative games with preplay communication. In the experiment subjects communicate byplain conversationprior to playing a simple game. In this setting, we find that the presumption ofindividualisticandindependentbehavior underlying the concept of Nash equilibrium is inappropriate. Instead, we observe behavior to becoordinatedandcorrelated. Statistical tests reject Nash equilibrium as an explanation of observed play. The coalition proof correlated equilibrium of the game, however, explains the data when the possibility of errors by players is introducedPublicad
Strategy-proof voting on compact ranges

Strategy-proof social choice functions are characterized for societies where the space of alternatives is any full dimensional compact subset of a Euclidean space and all voters have generalized single-peaked preferences. Our results build upon and extend those obtained for cartesian product ranges by Border and Jordan (1983). By admitting a large set of non-cartesian ranges, we give a partial answer to the major open question left unresolved in this pioneering article. We prove that our class is composed by generalized median voter schemes which satisfy an additional condition, called the intersection property (Barberà, Massó, and Neme (1997)
Endogenous Formation of Coalitions in Non-Cooperative Games

In this paper we extend the definitions of coalition-proof Nash equilibrium and communication-proof equilibrium to situations of partial communication. Then we use the model of endogenous formation of coalitions of Aumann and Myerson to find that one of these situations in which the corresponding equilibrium exists will be endogenously determined by the players in the gameFinancial support by DGES (Ministerio de Educación y Cultura, Spain), through projects PB95-0287 and UE95-0042 is gratefully acknowledged.Publicad
Conditional Universal Consistency

Players choose an action before learning an outcome chosen according to an unknown and history-dependent stochastic rule. Procedures that categorize outcomes, and use a randomized variation on fictitious play within each category are studied. These procedures are “conditionally consistent:” they yield almost as high a time-average payoff as if the player knew the conditional distributions of actions given categories. Moreover, given <i>any</i> alternative procedure, there is a conditionally consistent procedure whose performance is no more than epsilon worse regardless of the discount factor. We also discuss cycles, and argue that the time-average of play should resemble a correlated equilibrium.Economic
Simple Mechanisms to Implement the Core of College Admisions Problems

This paper analyzes simple mechanisms implementing (subselections of) the core correspondence of matching markets. We provide a sequential mechanism which mimics a matching procedure for many-to-one real life matching markets. We show that only core allocations should be attained when agents act strategically when faced with this mechanism. We also provide a second mechanism to implement the core correspondence in Subgame Perfect Equilibrium.Alcalde’s work is partially supported by the Institut Valencia
d’Investigacions Econòmiques and DGICYT under project PB 97–0131. Romero–Medina acknowledges
financial support from the Instituto de Estudios Fiscales and DGICYT under
project PB 92–0590.Publicad
An Experiment on the Hypothesis of Involuntary Truth-Signalling in Bargaining

AbstractWe examine face-to-face interaction in a two-person bargaining game with incomplete information in which each bargainer can either have costs to be subtracted from his/her bargaining agreement payoff or not. The bargaining events are observed by onlookers who guess the cost situations of the participants. The work of D. Gauthier (1978, Morals by Agreement. Oxford: Clarendon) and R. H. Frank (1988, Passions Within Reason: The Strategic Role of Emotions. New York: Norton) suggests that the onlookers' detection accuracy exceeds chance accuracy because of involuntary signals inherent in the behavior of the bargainers. It is shown that cost guesses are somewhat more accurate than chance. This effect, however, is entirely explainable by the onlookers' information about objective features of the bargaining process. Journal of Economic Literature Classification Numbers: C70, C91, D70, D82
Multiagent Cooperative Search for Portfolio Selection

We present a new multiagent model for the multiperiod portfolio selection problem. A system of cooperative agents divide initial wealth and follow individual worst-case optimal investment strategies from random portfolios, sharing their final profits and losses. The multiagent system achieves better average-case performance than a single agent with the same initial wealth in a simple stochastic market. A further increase in performance is achieved through communication of hints between agents and probabilistic strategy-switching. However, this explicit cooperation is redundant in a market that approximates the Capital Asset Pricing Model, a model of equilibrium stock price dynamics. Journal of Economic Literature Classification Numbers: C63, C73, D83, G11.Engineering and Applied Science
Maximal domain of preferences for the division problem

We are grateful to Carmen Beviá, Howard Petith, an associate editor, and two anonymous referees for their very helpful comments and suggestions. Financial support through a grant from the Programa de Cooperación Cientifica Iberoamericana is acknowledged. The work of Jordi Massó is also partially supported by Research Grants PB98-0870 from the Dirección General de Investigación Cientı́fica y Técnica, Spanish Ministry of Education, and SGR98-62 from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the Universitat Autònoma de Barcelona under a sabbatical fellowship from the Generalitat de CatalunyaThe division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawa's (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63
The scholarship assignment problem

There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome.Publicad
Backward induction and the game-theoretic analysis of chess

The paper scrutinizes various stylized facts related to the minmax theorem for chess. We first point out that, in contrast to the prevalent understanding, chess is actually an infinite game, so that backward induction does not apply in the strict sense. Second, we recall the original\ud
argument for the minmax theorem of chess – which is forward rather than backward looking. Then it is shown that, alternatively, the minmax theorem for the infinite version of chess can be reduced to the minmax theorem of the usually employed finite version. The paper concludes with a comment on Zermelo’s (1913) non-repetition theorem
Sexual maturity modifies the responsiveness of the pituitary-interrenal axis to stress in male rainbow trout

A significant reduction in stress-induced plasma cortisol levels is apparent in mature male rainbow trout compared to immature fish of both sexes and of the same age and strain. Mean plasma cortisol levels in groups of immature fish subjected to a standard 1h confinement stress were consistently higher (range 93.9 ± 4.9 - 114.8 ± 4.1 ng ml-1) than mean levels in mature males exposed to the same procedure (range 47.0 ± 4.3 - 71.7 ± 5.7 ng ml-1), throughout the 4 month period around spawning (p<0.001). Body weight was not found to be a significant determinant of post-stress cortisol level. The dissimilarity in plasma cortisol levels between mature and immature fish following confinement does not stem from differences in the dynamics of the response; during a 24h period of confinement the rate of elevation of plasma cortisol levels was similar for both mature male and immature fish but mature male fish attained a significantly lower peak cortisol level (51.6 ± 5.2 ng ml-1) than immature fish (89.5 ± 7.7 ng ml-1), a disparity which was maintained throughout the period of stress (p<0.05 - p<0.001). The reduced responsiveness of the interrenal tissue of mature male fish during stress appears to be modulated by the hypothalamus/pituitary. Plasma ACTH levels in mature male trout (44 ± 9 pg ml-1) are significantly lower than those of immature fish (71 ± 9 pg ml-1, p<0.01) within 30 min of the onset of confinement and remain so during a 3h period of confinement. These data suggest that the cortisol/ACTH feedback equilibrium has been modified in mature fish, to a lower "set point". Furthermore, although stress caused a significant decline of plasma α-MSH levels in both immature fish and mature males, N-acetyl-β-endorphin levels were reduced only in mature male fish during confinement stress