Sparse MDS Matrices over Small Fields: A Proof of the GM-MDS Conjecture

2021 ◽  
Vol 50 (4) ◽  
pp. 1248-1262
Author(s):  
Shachar Lovett
Keyword(s):  
Small Fields ◽  
Mds Conjecture

scholarly journals On additive MDS codes over small fields

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Simeon Ball ◽  
Guillermo Gamboa ◽  
Michel Lavrauw
Keyword(s):  
Mds Codes ◽  
Mds Code ◽  
Additive Codes ◽  
Non Linear ◽  
Small Fields ◽  
Mds Conjecture

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ C $\end{document}</tex-math></inline-formula> be a <inline-formula><tex-math id="M2">\begin{document}$ (n,q^{2k},n-k+1)_{q^2} $\end{document}</tex-math></inline-formula> additive MDS code which is linear over <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb F}_q $\end{document}</tex-math></inline-formula>. We prove that if <inline-formula><tex-math id="M4">\begin{document}$ n \geq q+k $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ k+1 $\end{document}</tex-math></inline-formula> of the projections of <inline-formula><tex-math id="M6">\begin{document}$ C $\end{document}</tex-math></inline-formula> are linear over <inline-formula><tex-math id="M7">\begin{document}$ {\mathbb F}_{q^2} $\end{document}</tex-math></inline-formula> then <inline-formula><tex-math id="M8">\begin{document}$ C $\end{document}</tex-math></inline-formula> is linear over <inline-formula><tex-math id="M9">\begin{document}$ {\mathbb F}_{q^2} $\end{document}</tex-math></inline-formula>. We use this geometrical theorem, other geometric arguments and some computations to classify all additive MDS codes over <inline-formula><tex-math id="M10">\begin{document}$ {\mathbb F}_q $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M11">\begin{document}$ q \in \{4,8,9\} $\end{document}</tex-math></inline-formula>. We also classify the longest additive MDS codes over <inline-formula><tex-math id="M12">\begin{document}$ {\mathbb F}_{16} $\end{document}</tex-math></inline-formula> which are linear over <inline-formula><tex-math id="M13">\begin{document}$ {\mathbb F}_4 $\end{document}</tex-math></inline-formula>. In these cases, the classifications not only verify the MDS conjecture for additive codes, but also confirm there are no additive non-linear MDS codes which perform as well as their linear counterparts. These results imply that the quantum MDS conjecture holds for <inline-formula><tex-math id="M14">\begin{document}$ q \in \{ 2,3\} $\end{document}</tex-math></inline-formula>.</p>

Problems and prospects of development of small fields in Russia

2019 ◽  
pp. 22-30
Author(s):  
A.F. Andreev ◽  
◽  
A.A. Daudova ◽  
A.A. Biketova ◽  
◽  
...  
Keyword(s):  
Small Fields

Mini Fracturing: A New Horizon of Breakthrough Integrated Technology for Small Fields.

2007 ◽  
Author(s):  
Chew Hong Sia ◽  
Azhar Md Ali ◽  
Nurul Ezalina Hamzah ◽  
Mohd Shafie Jumaat
Keyword(s):  
Integrated Technology ◽  
Small Fields

scholarly journals Field output factors for small fields: A large multicentre study

2021 ◽  
Vol 81 ◽  
pp. 191-196
Author(s):  
S. Dufreneix ◽  
J. Bellec ◽  
S. Josset ◽  
L. Vieillevigne
Keyword(s):  
Multicentre Study ◽  
Small Fields ◽  
Output Factors ◽  
Large Multicentre Study

scholarly journals Evaluation of Acuros® XB accuracy for static small fields dose calculations based on the IAEA/AAPM TRS-483 recommendation

2021 ◽  
Vol 89 ◽  
pp. 140-146
Author(s):  
José M. Lárraga-Gutiérrez ◽  
Olivia A. García-Garduñoa ◽  
José A. Herrera-González ◽  
Olga O. Galván de la Cruz
Keyword(s):  
Dose Calculations ◽  
Small Fields

scholarly journals Greater female first author citation advantages do not associate with reduced or reducing gender disparities in academia

2020 ◽  
Vol 1 (3) ◽  
pp. 1283-1297
Author(s):  
Mike Thelwall ◽  
Pardeep Sud
Keyword(s):  
United States ◽  
New Zealand ◽  
The United States ◽  
The United Kingdom ◽  
Science Technology ◽  
Small Fields ◽  
English Speaking ◽  
Author Citation ◽  
And Mathematics ◽  
Weak Tendency

Ongoing problems attracting women into many Science, Technology, Engineering and Mathematics (STEM) subjects have many potential explanations. This article investigates whether the possible undercitation of women associates with lower proportions of, or increases in, women in a subject. It uses six million articles published in 1996–2012 across up to 331 fields in six mainly English-speaking countries: Australia, Canada, Ireland, New Zealand, the United Kingdom and the United States. The proportion of female first- and last-authored articles in each year was calculated and 4,968 regressions were run to detect first-author gender advantages in field normalized article citations. The proportion of female first authors in each field correlated highly between countries and the female first-author citation advantages derived from the regressions correlated moderately to strongly between countries, so both are relatively field specific. There was a weak tendency in the United States and New Zealand for female citation advantages to be stronger in fields with fewer women, after excluding small fields, but there was no other association evidence. There was no evidence of female citation advantages or disadvantages to be a cause or effect of changes in the proportions of women in a field for any country. Inappropriate uses of career-level citations are a likelier source of gender inequities.

scholarly journals Does Habitat Diversity Modify the Dietary and Reproductive Response to Prey Fluctuations in a Generalist Raptor Predator, the Eurasian Buzzard Buteo buteo?

Birds ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 114-126
Author(s):  
Marek Panek
Keyword(s):  
Habitat Quality ◽  
Breeding Success ◽  
Common Vole ◽  
Habitat Diversity ◽  
Crop Fields ◽  
Buteo Buteo ◽  
Nestling Diet ◽  
Reproductive Response ◽  
Agricultural Habitat ◽  
Small Fields

Predators can modify their diet and demography in response to changes in food availability and habitat quality. I tested the prediction that some species can change their predation pattern, between specialist type and generalist type, depending on the complexity of habitat structure. It was hypothesized that their dietary response is stronger in diversified habitats than in simplified ones, but the opposite tendency occurs in the case of reproductive response. The nestling diet and breeding success of the Eurasian Buzzard Buteo buteo, the abundance of its main prey (the common vole Microtus arvalis), and that of the most important alternative prey group (passerines) were estimated over ten years in two types of agricultural habitat in western Poland, i.e., in the diversified habitat of small fields and the simplified habitat of large fields. The vole abundance was higher in large fields, but the abundance of passerines was greater in small fields. The frequency of voles in the Eurasian Buzzard nestling diet was higher in large fields than in small fields and increased with the abundance of this prey in crop fields. However, no difference in the relationship between the vole frequency in the diet of Eurasian Buzzards and the abundance of voles was found between the two habitat types. The breeding success of Eurasian Buzzards was dependent on the vole abundance, but this relationship did not differ between the two field types. It seems that the pattern of dietary and reproductive response of Eurasian Buzzards depends on the actual availability of individual prey species, which can be modified by habitat quality, rather than on relative prey abundance.

PD-0037 HIGH PRECISION OUTPUT FACTOR RESULTS FOR THE CYBERKNIFE IRIS COLLIMATOR SMALL FIELDS

2012 ◽  
Vol 103 ◽  
pp. S14-S15
Author(s):  
A. Moutsatsos ◽  
L. Petrokkokinos ◽  
K. Zourari ◽  
C. Antypas ◽  
P. Papagiannis ◽  
...  
Keyword(s):  
High Precision ◽  
Output Factor ◽  
Small Fields
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