Asymptotics of the minimal distance of quadratic residue codes Jos´ e Felipe Voloch The binary quadratic residue codes are defined as follows. Given a prime p ≡

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Double Circulant Quadratic Residue Codes ∗ Tor Helleseth †

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ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS SHIN HATTORI Abstract. Let p be a rational prime. Let F be a totally real number field such that F is unramified over

Source URL: www2.math.kyushu-u.ac.jp

• Algebra
• Mathematics
• Abstract algebra
• Modular forms
• Field theory
• Analytic number theory
• Operator theory
• Algebraic geometry
• Eigenform
• P-adic modular form
• Elliptic curve
• Valuation

ETH Zurich, Department of Computer Science FS 2015 Prof. Dr. Ueli Maurer Dr. Martin Hirt Sandro Coretti

Source URL: www.crypto.ethz.ch

• Computational complexity theory
• Complexity classes
• IP
• Proof of knowledge
• NP
• Soundness
• Interactive proof system
• PSPACE
• Zero-knowledge proof
• Probabilistic complexity theory
• Mathematical proof
• Quadratic residue

SMOOTH NUMBERS AND THE QUADRATIC SIEVE Carl Pomerance When faced with a large number n to factor, what do you do first? You might say “Look at the last digit,” with the idea of cheaply pulling out possible factors of

Source URL: www.mat.uniroma2.it

• Mathematics
• Integer factorization algorithms
• Number theory
• Quadratic sieve
• Special number field sieve
• Quadratic residue
• General number field sieve
• Prime number
• Lenstra elliptic curve factorization
• Sieve of Eratosthenes
• Euclidean algorithm
• Prime-counting function

ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS SHIN HATTORI Abstract. Let p be a rational prime. Let F be a totally real number field such that F is unramified over

Source URL: www2.math.kyushu-u.ac.jp

• Algebra
• Mathematics
• Abstract algebra
• Operator theory
• Field theory
• Analytic number theory
• Modular forms
• Algebraic geometry
• Eigenform
• Elliptic curve
• Valuation
• Algebraic number field

Annales Univ. Sci. Budapest., Sect. Comp–27 PRIMALITY PROOFS WITH ELLIPTIC CURVES: HEURISTICS AND ANALYSIS Wieb Bosma, Eric Cator (Nijmegen, The Netherlands)

Source URL: www.math.ru.nl

• Abstract algebra
• Algebra
• Mathematics
• Primality tests
• Finite fields
• Elliptic curves
• Elliptic curve primality
• Group theory
• Elliptic curve
• Lenstra elliptic curve factorization
• Quadratic residue
• Prime number

ETH Zurich, Department of Computer Science FS 2015 Prof. Dr. Ueli Maurer Dr. Martin Hirt Sandro Coretti

Source URL: www.crypto.ethz.ch

• Cryptography
• Modular arithmetic
• Zero-knowledge proof
• Quadratic residue
• RSA
• FeigeFiatShamir identification scheme
• IP
• Public-key cryptography

Computing the minimal distance of cyclic codes Jos´ e Felipe Voloch Abstract: We describe an algorithm that improves on the standard algorithm for computing the minimal distance of cyclic codes. Keywords: cyclic codes,

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• Coding theory
• Cyclic code
• BCH code
• Polynomial code
• Quadratic residue
• Linear code
• ReedSolomon error correction

Automorphism groups of extremal self-dual binary linear codes Martino Borello Università degli Studi di Milano-Bicocca The 11

Source URL: www.math.uni-magdeburg.de

• Coding theory
• Abstract algebra
• Morphisms
• Finite groups
• Automorphism
• Symmetry
• Dual code
• Elementary abelian group
• Quadratic residue code
• Duality