Výsledky vyhledávání - "Ball, Simeon Michael"

Autor: Ball, Simeon Michael, Adriaensen, Sam

We prove that an additive code over a finite field which has a few projections which are equivalent to a linear code is itself equivalent to a linear code, providing the code is not too short.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od______3484::48cc5a4bc4e7e77482ca92d9fccd61b6
https://hdl.handle.net/2117/387261

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A polynomial-time reduction from the multi-graph isomorphism problem to additive codeequivalence

Autor: Ball, Simeon Michael, Dixon, James

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

We present a polynomial-time reduction from the multi-graph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of the field with two elements.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::03598c7d5f8cedf4c359151a1b9ad6d2
http://hdl.handle.net/2117/364757

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The polynomial method in Galois geometries

Autor: Ball, Simeon Michael

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

The polynomial method refers to the application of polynomials to combinatorial problems. The method is particularly effective for Galois geometries and a number of problems and conjectures have been solved using the polynomial method. In many cases

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::dfa3fc72f9160fab977ba090fb016d6a
https://hdl.handle.net/2117/18846

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Punctured combinatorial Nullstellensätze

Autor: Ball, Simeon Michael|||0000-0003-4845-2084, Serra Albó, Oriol|||0000-0001-8561-4631

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

In this article we present a punctured version of Alon's Nullstellensatz which states that if $f$ vanishes at nearly all, but not all, of the common zeros of some polynomials $g_1(X_1),\ldots,g_n(X_n)$ then every $I$-residue of $f$, where the ideal $

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::45d9fc21f97f469bab4852ba602f00bb
https://hdl.handle.net/2117/1404

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On the graph of a function over a prime field whose small powers have bounded degree

Autor: Ball, Simeon Michael|||0000-0003-4845-2084, Gács, Andras

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Let $f$ be a function from a finite field ${\mathbb F}_p$ with a prime number $p$ of elements, to ${\mathbb F}_p$. In this article we consider those functions $f(X)$ for which there is a positive integer $n > 2\sqrt{p-1}-\frac{11}{4}$ with the proper

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::3bc8a60db7e2cc25570a099ddab33c75
https://hdl.handle.net/2117/1403

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Symplectic spreads and permutation polynomials

Autor: Ball, Simeon Michael, Zieve, Michael

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF(q) and vice-versa. This leads to an algebraic proof of the existence of the Tits-L¨uneburg spread of W(22

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::4c923dacce6d5f64c0112515386457d2
http://hdl.handle.net/2117/18893

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Quantum low density parity check codes

Autor: Popatia, Tabriz

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Low density Parity Check (LDPC) Codes are asymptotically good codes with a fast decoding algorithm, and hence have extensive applications. A lot of work has been done on constructing a quantum code with LDPC properties. Recent breakthroughs show that

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::8b1a21f10f0ca77f2689e04fb7292a97
http://hdl.handle.net/2117/372044

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The geometry of quantum codes

Autor: Puig Pericas, Pablo

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Quantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::d10a379152e5bf2a85f5e6d5ecd72af9
https://hdl.handle.net/2117/349594

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Low density parity check codes

Autor: Ortega Sánchez-Colomer, Tomás

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

Low Density Parity Check codes, LDPCs for short, are a family of codes which have shown near optimal error-correcting capabilites. They were proposed in 1963 by Robert Gallager in his PhD thesis. While he proved that probabilistic constructions of ra

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::95403a879afc39f74792e7c9c16adee7
http://hdl.handle.net/2117/349213

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