Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2016, Volume 436, Issue 1, pp. 489 - 500

Let α be a totally positive algebraic integer, and define its absolute trace to be Tr(α)deg(α), the trace of α divided by the degree of α. Elementary...

Totally positive algebraic number | Minimal polynomial | Schur–Siegel–Smyth trace problem | Schur-Siegel-Smyth trace problem | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE ALGEBRAIC-INTEGERS | VALUES

Totally positive algebraic number | Minimal polynomial | Schur–Siegel–Smyth trace problem | Schur-Siegel-Smyth trace problem | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE ALGEBRAIC-INTEGERS | VALUES

Journal Article

Journal of Number Theory, ISSN 0022-314X, 03/2016, Volume 160, pp. 409 - 417

In 1993 Estes and Guralnick conjectured that any totally real separable monic polynomial with rational integer coefficients will occur as the minimal...

Minimal polynomials | Salem numbers | POLYNOMIALS | MATHEMATICS

Minimal polynomials | Salem numbers | POLYNOMIALS | MATHEMATICS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 227 - 230

Let A be a connected integer symmetric matrix, i.e., A=(aij)∈Mn(Z) for some n, A=AT, and the underlying graph (vertices corresponding to rows, with vertex i...

Trace problem | Minimal polynomials | Integer symmetric matrices | MATHEMATICS, APPLIED | ALGEBRAIC-INTEGERS | SALEM-NUMBERS

Trace problem | Minimal polynomials | Integer symmetric matrices | MATHEMATICS, APPLIED | ALGEBRAIC-INTEGERS | SALEM-NUMBERS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2011, Volume 57, Issue 3, pp. 1530 - 1547

Let p = ef + 1 be an odd prime for some e and e and let f, be the finite field with F p elements. In this paper, we explicitly describe the trace...

Correlation | linear complexity | Generators | e th residue cyclic difference sets | Complexity theory | Indexes | Hamming weight | trace representations | Binary sequences with two-level autocorrelation | Polynomials | cyclic difference sets | Binary sequences | minimal polynomials | eth residue cyclic difference sets | EXISTENCE | IDEAL AUTOCORRELATION | HADAMARD DIFFERENCE SETS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | LEGENDRE SEQUENCES | PSEUDORANDOM SEQUENCES | Sequences (Mathematics) | Research

Correlation | linear complexity | Generators | e th residue cyclic difference sets | Complexity theory | Indexes | Hamming weight | trace representations | Binary sequences with two-level autocorrelation | Polynomials | cyclic difference sets | Binary sequences | minimal polynomials | eth residue cyclic difference sets | EXISTENCE | IDEAL AUTOCORRELATION | HADAMARD DIFFERENCE SETS | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | LEGENDRE SEQUENCES | PSEUDORANDOM SEQUENCES | Sequences (Mathematics) | Research

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 04/2009, Volume 78, Issue 266, pp. 1119 - 1125

Explicit auxiliary functions can be used in the ``Schur-Siegel- Smyth trace problem''. In the previous works, these functions were constructed only with...

Integers | Local minimum | Numbers | Algebra | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Complex roots | Degrees of polynomials | POLYNOMIALS | COEFFICIENTS | MATHEMATICS, APPLIED | NUMBERS

Integers | Local minimum | Numbers | Algebra | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Complex roots | Degrees of polynomials | POLYNOMIALS | COEFFICIENTS | MATHEMATICS, APPLIED | NUMBERS

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2019, Volume 65, Issue 4, pp. 2101 - 2106

In this paper, we construct some class of explicit subcovers of the curve X n,r defined over F q(n) by affine equation y q(n-1) + ··· + y q + y = x q(n-r)+1 -...

Codes | AG codes | subcover | Polynomials | Trace-defining curves | Topology | Mathematical model | Weierstrass semigroup | CASTLE | COMPUTER SCIENCE, INFORMATION SYSTEMS | MINIMUM DISTANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Formulas (mathematics)

Codes | AG codes | subcover | Polynomials | Trace-defining curves | Topology | Mathematical model | Weierstrass semigroup | CASTLE | COMPUTER SCIENCE, INFORMATION SYSTEMS | MINIMUM DISTANCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Formulas (mathematics)

Journal Article

Finite Fields and their Applications, ISSN 1071-5797, 11/2008, Volume 14, Issue 4, pp. 1002 - 1009

The extension field F where q is a prime divisor of (P - 1), has a unique structure. This paper describes this unique structure and uses it to derive formulas...

Trace | Reciprocal polynomial | Root computation

Trace | Reciprocal polynomial | Root computation

Journal Article

Finite Fields and Their Applications, ISSN 1071-5797, 2008, Volume 14, Issue 4, pp. 1002 - 1009

The extension field F P q where q is a prime divisor of ( P − 1 ) , has a unique structure. This paper describes this unique structure and uses it to derive...

Trace | Reciprocal polynomial | Root computation

Trace | Reciprocal polynomial | Root computation

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2006, Volume 75, Issue 253, pp. 385 - 393

For all totally positive algebraic numbers \alpha except a finite number of explicit exceptions, the following inequality holds: \[...

Integers | Local minimum | Algebra | Heuristics | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Coefficients | Algebraic conjugates | MATHEMATICS, APPLIED

Integers | Local minimum | Algebra | Heuristics | Mathematical tables | Polynomials | Mathematical functions | Mathematical inequalities | Coefficients | Algebraic conjugates | MATHEMATICS, APPLIED

Journal Article

Journal of Number Theory, ISSN 0022-314X, 02/2016, Volume 159, pp. 402 - 425

We establish a relation between minimal value set polynomials defined over Fq and certain q-Frobenius nonclassical curves. The connection leads to a...

Frobenius nonclassical curve | Finite field | Minimal value set polynomial | POLYNOMIALS | TRACE | MATHEMATICS | GENERALIZED HERMITIAN CODES | FINITE-FIELDS | NORM | PLANE-CURVES

Frobenius nonclassical curve | Finite field | Minimal value set polynomial | POLYNOMIALS | TRACE | MATHEMATICS | GENERALIZED HERMITIAN CODES | FINITE-FIELDS | NORM | PLANE-CURVES

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2018, Volume 108, Issue 3, pp. 633 - 678

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this...

Calabi–Yau varieties | Milnor fibration | 37J05 | Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson homology | 14F10 | Milnor number | Physics | Poisson varieties | Geometry | Symplectic resolutions | Twistor deformations | 32S20 | D-modules | Poisson traces | Group Theory and Generalizations | Kostka polynomials | Hamiltonian flow | Complete intersections | COMPLEX | HOLONOMIC SYSTEMS | SINGULARITIES | LIE-ALGEBRA | VARIETIES | CHEREDNIK ALGEBRAS | Calabi-Yau varieties | PHYSICS, MATHEMATICAL | REPRESENTATION-THEORY | COHOMOLOGY | QUANTIZATION | HOMOLOGY | Algebra

Calabi–Yau varieties | Milnor fibration | 37J05 | Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson homology | 14F10 | Milnor number | Physics | Poisson varieties | Geometry | Symplectic resolutions | Twistor deformations | 32S20 | D-modules | Poisson traces | Group Theory and Generalizations | Kostka polynomials | Hamiltonian flow | Complete intersections | COMPLEX | HOLONOMIC SYSTEMS | SINGULARITIES | LIE-ALGEBRA | VARIETIES | CHEREDNIK ALGEBRAS | Calabi-Yau varieties | PHYSICS, MATHEMATICAL | REPRESENTATION-THEORY | COHOMOLOGY | QUANTIZATION | HOMOLOGY | Algebra

Journal Article

Asian-European Journal of Mathematics, ISSN 1793-5571, 03/2015, Volume 8, Issue 1

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2019, Volume 65, Issue 4, pp. 2593 - 2602

We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for...

Computers | quantum codes | Quantum computing | trace | IEEE Sections | Hermitian duality | Evaluation codes | subfield-subcodes | Linear codes | Generators | Error correction codes | Indexes | ERROR-CORRECTING CODES | STABILIZER CODES | MDS CODES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Codes | Roots | Binary system | Polynomials | Fields (mathematics) | Orthogonality

Computers | quantum codes | Quantum computing | trace | IEEE Sections | Hermitian duality | Evaluation codes | subfield-subcodes | Linear codes | Generators | Error correction codes | Indexes | ERROR-CORRECTING CODES | STABILIZER CODES | MDS CODES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Codes | Roots | Binary system | Polynomials | Fields (mathematics) | Orthogonality

Journal Article

Acta Mathematica Vietnamica, ISSN 0251-4184, 3/2016, Volume 41, Issue 1, pp. 171 - 181

First, we study linear equations over finite fields in general. An explicit formula for a common period is found for every solution of a linear difference...

Trace representation | Characteristic equations | Jordan multiplicative decomposition | Lucas’ congruence | 12Y05 | 12E20 | Mathematics, general | Mathematics | Max-sequences | Minimal polynomial

Trace representation | Characteristic equations | Jordan multiplicative decomposition | Lucas’ congruence | 12Y05 | 12E20 | Mathematics, general | Mathematics | Max-sequences | Minimal polynomial

Journal Article

Experimental Mathematics, ISSN 1058-6458, 01/2014, Volume 23, Issue 1, pp. 1 - 5

In this paper, we give a list of monic integer polynomials of smallest possible trace, irreducible, of degree 16, and having all roots real and positive....

Schur-Siegel-Smyth Trace Problem | polynomials with minimal trace | auxiliary functions | Auxiliary functions | Polynomials with minimal trace | MATHEMATICS | 11C08 | 11R09 | 11S05 | 26C10 | 90C11 | 12D10 | ALGEBRAIC-INTEGERS | Continental interfaces, environment | Sciences of the Universe | Environmental Sciences

Schur-Siegel-Smyth Trace Problem | polynomials with minimal trace | auxiliary functions | Auxiliary functions | Polynomials with minimal trace | MATHEMATICS | 11C08 | 11R09 | 11S05 | 26C10 | 90C11 | 12D10 | ALGEBRAIC-INTEGERS | Continental interfaces, environment | Sciences of the Universe | Environmental Sciences

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2006, Volume 52, Issue 6, pp. 2608 - 2623

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing...

Laboratories | Ad hoc networks | network optimization | multicast | Multicast algorithms | Unicast | Wireless networks | dynamic multicast groups | distributed algorithms | Network coding | Broadcasting | Polynomials | Computer networks | Dynamic programming | Communication networks | Multicast | Network optimization | Dynamic multicast groups | Distributed algorithms | network coding | RESOURCE-ALLOCATION | communication networks | COMPUTER SCIENCE, INFORMATION SYSTEMS | wireless networks | ALGORITHMS | ad hoc networks | ENGINEERING, ELECTRICAL & ELECTRONIC | Wireless local area networks (Computer networks) | Packet switching | Analysis | Networks | Algorithms | Dynamics | Packets (communication) | Decentralized | Joints

Laboratories | Ad hoc networks | network optimization | multicast | Multicast algorithms | Unicast | Wireless networks | dynamic multicast groups | distributed algorithms | Network coding | Broadcasting | Polynomials | Computer networks | Dynamic programming | Communication networks | Multicast | Network optimization | Dynamic multicast groups | Distributed algorithms | network coding | RESOURCE-ALLOCATION | communication networks | COMPUTER SCIENCE, INFORMATION SYSTEMS | wireless networks | ALGORITHMS | ad hoc networks | ENGINEERING, ELECTRICAL & ELECTRONIC | Wireless local area networks (Computer networks) | Packet switching | Analysis | Networks | Algorithms | Dynamics | Packets (communication) | Decentralized | Joints

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2011, Volume 57, Issue 2, pp. 601 - 620

This paper offers new insights into expanded cyclic and Reed-Solomon codes. First, we present a new description of general expanded codes defined over GF( qm...

binary expanded Reed-Solomon codes | block-bidiagonal structure | expanded codes | Special issues and sections | effective trellis dimension | trace-dual subbasis | product basis | Generators | Indexes | basis | expanded cyclic codes | Asymptotic minimum distance bound | dual basis | Maximum likelihood decoding | dual expanded codes | subspace subcodes | Polynomials | Parity check codes | binary expanded Reed - Solomon codes | DISTANCE | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Q-ARY IMAGE | WEIGHT-ENUMERATOR | LINEAR BLOCK-CODES | Reed-Solomon codes | Coding theory | Research | Methods | Codes | Algorithms | Conjugates | Asymptotic properties | Roots | Spectra | Subspaces | Parity

binary expanded Reed-Solomon codes | block-bidiagonal structure | expanded codes | Special issues and sections | effective trellis dimension | trace-dual subbasis | product basis | Generators | Indexes | basis | expanded cyclic codes | Asymptotic minimum distance bound | dual basis | Maximum likelihood decoding | dual expanded codes | subspace subcodes | Polynomials | Parity check codes | binary expanded Reed - Solomon codes | DISTANCE | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Q-ARY IMAGE | WEIGHT-ENUMERATOR | LINEAR BLOCK-CODES | Reed-Solomon codes | Coding theory | Research | Methods | Codes | Algorithms | Conjugates | Asymptotic properties | Roots | Spectra | Subspaces | Parity

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2013, Volume 141, Issue 9, pp. 2963 - 2978

We provide a necessary and sufficient condition for a simple object in a pivotal \Bbbk minimal model in conformal field theory, and quantum groups at a root of...

DIMENSIONAL HOPF-ALGEBRAS | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | LIE SUPER-ALGEBRAS | REPRESENTATIONS | INVARIANTS | DELIGNES CATEGORY | SUPERALGEBRAS | FORMULA | FINITE TENSOR CATEGORIES | CHARACTERS | Quantum Algebra | Mathematics | Representation Theory

DIMENSIONAL HOPF-ALGEBRAS | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | LIE SUPER-ALGEBRAS | REPRESENTATIONS | INVARIANTS | DELIGNES CATEGORY | SUPERALGEBRAS | FORMULA | FINITE TENSOR CATEGORIES | CHARACTERS | Quantum Algebra | Mathematics | Representation Theory

Journal Article

2014 IEEE International Conference on Information and Automation (ICIA), 07/2014, pp. 137 - 140

The paper described a novel method of computing the trace of an element from a given finite field GF(p n ). By applying the Newton Formula, this method shows a...

Finite Fields | Abstracts | Educational institutions | Minimal Polynomial | Polynomials | Finite element analysis | Cryptography | Galois fields | Trace Computation

Finite Fields | Abstracts | Educational institutions | Minimal Polynomial | Polynomials | Finite element analysis | Cryptography | Galois fields | Trace Computation

Conference Proceeding

Taiwanese Journal of Mathematics, ISSN 1027-5487, 2/2008, Volume 12, Issue 1, pp. 245 - 253

We study polynomials over finite fields with a given value set. By constructing relations among the coefficients of Lagrange Interpolation Formula of these...

Integers | Cardinality | Mathematical sets | Polynomials | Mathematics | Coefficients | Degrees of polynomials | Trace | Finite field | Minimal value set polynomial | Value set | MATHEMATICS | trace | minimal value set polynomial | finite field | value set

Integers | Cardinality | Mathematical sets | Polynomials | Mathematics | Coefficients | Degrees of polynomials | Trace | Finite field | Minimal value set polynomial | Value set | MATHEMATICS | trace | minimal value set polynomial | finite field | value set

Journal Article

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