Publications related to Coding Theory and Bilinear Complexity

Few distinct distances implies no heavy lines or circles

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...

Springer Heidelberg2016

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Distinct Values Of Bilinear Forms On Algebraic Curves

Frank de Zeeuw, Adrian Claudiu Valculescu

Let B-M : C x C -> C be a bilinear form B-M(p, q) - p(T)Mq, with an invertible matrix M is an element of C-2x2. We prove that any finite set S contained in an irreducible algebraic curve C of degree d in C determines Omega(d)(vertical bar S vertical bar(4/ ...

Univ Calgary, Dept Math & Statistics2016

The xi-stability on the affine grassmannian

Zongbin Chen

We introduce a notion of xi-stability on the affine grassmannian (SIC) for the classical groups, this is the local version of the xi-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient ( ...

Springer Heidelberg2015

Algebraic twists of modular forms and Hecke orbits

Philippe Michel

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistri ...

Springer Verlag2015

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Robert Granger

In this paper we present a new multiplication algorithm for residues modulo the Mersenne prime

2^{521}−1

. Using this approach, on an Intel Haswell Core i7-4770, constant-time variable-base scalar multiplication on NIST’s (and SECG’s) curve P-521 requires ...

Springer Berlin Heidelberg2015

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

In this paper, we extend the theory of sampling signals with finite rate of innovation (FRI) to a specific class of two-dimensional curves, which are defined implicitly as the zeros of a mask function. Here the mask function has a parametric representation ...

Institute of Electrical and Electronics Engineers2014

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming, Georgios Karakonstantis

Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications. Unfortunately, the successiv ...

2014

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

Andreas Peter Burg, Alexios Konstantinos Balatsoukas Stimming, Georgios Karakonstantis

Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications. Unfortunately, the successiv ...

Ieee2014

Coding Theory and Bilinear Complexity

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Few distinct distances implies no heavy lines or circles

Computational Aspects of Jacobians of Hyperelliptic Curves

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Distinct Values Of Bilinear Forms On Algebraic Curves

The xi-stability on the affine grassmannian

Algebraic twists of modular forms and Hecke orbits

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Sampling Curves with Finite Rate of Innovation

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

Computational Aspects of Jacobians of Hyperelliptic Curves

Distinct Values Of Bilinear Forms On Algebraic Curves

Few distinct distances implies no heavy lines or circles

Faster ECC over $\mathbb{F}_{2^{521}-1}$

Algebraic twists of modular forms and Hecke orbits

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

The xi-stability on the affine grassmannian

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes

Sampling Curves with Finite Rate of Innovation

Enabling Complexity-Performance Trade-Offs for Successive Cancellation Decoding of Polar Codes