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Record W1984035421 · doi:10.4153/cmb-2011-160-x

Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields

2011· article· en· W1984035421 on OpenAlexvenueno aff
Lê Anh Vinh

Bibliographic record

VenueCanadian Mathematical Bulletin · 2011
Typearticle
Languageen
FieldComputer Science
TopicCoding theory and cryptography
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsFinite fieldCardinality (data modeling)Pairwise comparisonBilinear formCombinatoricsInteger (computer science)Field (mathematics)Degenerate energy levelsDiscrete mathematicsPure mathematicsStatistics

Abstract

fetched live from OpenAlex

Abstract Given a positive integer n , a finite field of q elements ( q odd), and a non-degenerate symmetric bilinear form B on , we determine the largest possible cardinality of pairwise B -orthogonal subsets , that is, for any two vectors x , y ∈ Ε, one has B ( x , y ) = 0.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.224
Threshold uncertainty score0.995

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0060.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.025
GPT teacher head0.203
Teacher spread0.178 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations9
Published2011
Admission routes1
Has abstractyes

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