Bounds for the $$l_1$$ l 1 -distance of q-ary lattices obtained via Constructions D, D $$^{'}$$ ′ and $$\overline{\text{ D }}$$ D ¯

Strey, Eleonesio; Costa, Sueli I. R.

doi:10.1007/s40314-017-0453-x

Cited by 3 publications

(12 citation statements)

References 25 publications

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“…As an employed member of the district where the study was conducted, I am cognizant of my unintended positionality and reflexivity that could impact the research. According to Ary et al (2019), practicing reflexivity, a form of self-reflection behavior to avoid unintended personal bias, supported the ethical standards for conducting the qualitative portion of this study. Because the qualitative data collection procedures of this mixed-methods research design required me to engage as an active participant in conducting the focus group interviews, I needed to practice reflexivity as an embedded and ongoing process.…”

Section: Researcher Positionalitymentioning

confidence: 90%

“…As demonstrated in Figure 2, quantitative and qualitative research methods were used concurrently in this study. Quantitative research methods include the measurement of data through scientific inquiry to determine if a correlation exists between two variables (Ary et al, 2019). For this study, quantitative methods included a survey given to teachers to gather their perceptions about PLCs and the supportive conditions for PLCs for improved teacher instructional practices.…”

Section: Methodsmentioning

confidence: 99%

“…The ethical and legal assurances for conducting a study are an integral part of the research process (Ary et al, 2019). Ethical standards and researcher positionality are explained.…”

Section: Ethical Assurancesmentioning

confidence: 99%

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Professional Learning Communities and the Supportive Conditions for Improved Teacher Instructional Practices

Parham

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The purpose of the study was to examine and evaluate the extent to which the supportive conditions (collaboration, teacher efficacy, shared leadership, and trust) were present in the district's current professional learning communities (PLCs) model, and whether teachers perceived the supportive conditions to be related to improving their instructional practices. This mixed-methods study used Pearson correlation coefficient, multiple regression, and focus group interviews to concurrently triangulate data to answer the research questions. The sample from this study was identified from 600 middle school teachers. Survey participants included 139 teachers and each of the four focus group interviews contained 6 teachers for a total of 24 teachers. Of the four supporting conditions analyzed, trust generated the highest mean (M = 3.41). Results from this study indicate that the supportive conditions for PLCs have a strong correlation (0.10) with the studied district's current PLC model and each specific supporting condition elicits a targeted aspect of professional learning that has a significant impact on teacher instructional practices. Recommendations for future studies include the expansion of this study to include elementary and high school participants and to extend this study to a larger scope of interested districts seeking to improve their PLC structures for improved teacher instructional practices. Expanding this research could build upon the current body of literature as it relates to PLCs, professional learning, and student achievement.

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Section: Researcher Positionalitymentioning

confidence: 90%

Section: Methodsmentioning

confidence: 99%

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Professional Learning Communities and the Supportive Conditions for Improved Teacher Instructional Practices

Parham

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“…No Capítulo 3, são apresentadas nossas principais contribuições que incluem os resultados de [41][42][43][44]. Na Seção 3.1, estudamos a Construção A para códigos lineares qários (q ∈ N) e mostramos que o reticulado tridimensional de maior densidade na métrica da soma pode ser obtido via Construção A. Na Seção 3.2.1, estendemos a Construção D para códigos lineares q-ários (q ∈ N) e mostramos que a mesma sempre produz um reticulado.…”

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“…Os resultados deste capítulo incluem os apresentados em [41,42], os quais possuem versões preliminares [43,44].…”

Section: Reticulados Obtidos a Partir De Códigos Linearesunclassified

Construções de reticulados a partir de códigos q-ários

Strey¹

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Reticulados vêm sendo utilizados na abordagem de vários problemas em códigos corretores de erros e criptografia. Este trabalho foca em construções de reticulados a partir de códigos lineares q-ários. Construções D, D 1 e D e vários resultados são estendidos de códigos lineares binários para códigos lineares q-ários, q P N. Definimos a adição zeroum em Z n q e mostramos que a Construção D produz um reticulado se, e somente se, a cadeia de códigos utilizada é fechada sob esta adição. Fórmulas fechadas ou limitantes para a distância da soma mínima de reticulados obtidos via Construções D, D 1 e D são fornecidos. Introduzimos a Construção A 1 a partir de códigos lineares sobre o anel quociente Z q rXs{pX a q e mostramos que a mesma produz um reticulado se, e somente se, o código utilizado é fechado sob a adição zero-um deslocada. Conexões entre as construções supracitadas também são fornecidas.

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On Lattice Constructions D and D' from q-ary Linear Codes

Silva,

de Souza,

Strey

et al. 2023

Communications in Mathematics

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Multilevel lattice codes, such as those associated to Constructions $C$, $\overline{D}$, D and D', have relevant applications in communications. In this paper, we investigate some properties of lattices obtained via Constructions D and D' from $q$-ary linear codes. Connections with Construction A, generator matrices, expressions and bounds for the lattice volume and minimum distances are derived. Extensions of previous results regarding construction and decoding of binary and $p$-ary linear codes ($p$ prime) are also presented.

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Bounds for the $$l_1$$ l 1 -distance of q-ary lattices obtained via Constructions D, D $$^{'}$$ ′ and $$\overline{\text{ D }}$$ D ¯

Cited by 3 publications

References 25 publications

Professional Learning Communities and the Supportive Conditions for Improved Teacher Instructional Practices

Professional Learning Communities and the Supportive Conditions for Improved Teacher Instructional Practices

Construções de reticulados a partir de códigos q-ários

On Lattice Constructions D and D' from q-ary Linear Codes

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