Pith. Sign in

RECORD

Line Polar Grassmann Codes of Orthogonal Type

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Ilaria Cardinali, Luca Giuzzi, Antonio Pasini

Combinatorics · Submitted 23 Jul 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1407.6149 (version 2)
Pith ID4MAR57QD, Pith's permanent record of this paper and its review
CitationAntonio Pasini, Ilaria Cardinali, Luca Giuzzi. "Line Polar Grassmann Codes of Orthogonal Type." arXiv:1407.6149 (2014). https://pith.science/paper/4MAR57QD
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,630 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.69 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.41 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. background 1.00 0.05 0.02 asserted 0.97
s1 Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. background 1.00 0.04 0.02 unclear 0.68
s2 They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. background 1.00 0.07 0.03 asserted 1.00
s3 In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd. contribution 0.63 0.96 0.94 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Polar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for $q$ odd.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Builds on it 1 paper
  • The aim of the present paper is to provide results analogous to those of [ref] for codes arising from the Plücker embedding of $k$–Grassmannians of symplectic type.

    Minimum distance of Symplectic Grassmann codes · Introduction · 0.91

Uses its method or tool 1 paper
  • It is well known that any bilinear alternating form $θ$ determines an hyperplane of $⋀^2 V$ and conversely; hence, the minimum distance of $(n,2)$ can be deduced from the maximum number of lines which are simultaneously totally isotropic for both the forms $θ$ and $σ$, under the assumption $θ≠σ.$ In order to determine this number we follow an approach similar to that of [ref] .

    Minimum distance of Symplectic Grassmann codes · Line Symplectic Grassmann Codes · 0.98

Cites it as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.