Binary additive MRD codes with minimum distance $$n-1$$ n - 1 must contain a semifield spread set

Sheekey, John

doi:10.1007/s10623-019-00637-6

Cited by 2 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Similarly, an r-dimensional subspace of \BbbF n\times n q defines | GL r (q)| different r \times n \times n tensors. As proved in [42,Theorem 4], the set of tensors obtained from n-dimensional subspaces of \BbbF r\times n q with minimum rank-distance r coincides with the set of tensors obtained from r-dimensional subspaces of \BbbF n\times n q with minimum rankdistance n. Counting the number of such tensors in two ways gives the identity in the statement.…”

Section: Comparisons and State Of The Artmentioning

confidence: 80%

“…Redistribution subject to SIAM license or copyright; see https://epubs.siam.org/terms-privacy Proof. Following the proof of [42,Theorem 4], an n-dimensional subspace of \BbbF r\times n q defines | GL n (q)| different r \times n \times n tensors: one for each ordered basis of the subspace. Similarly, an r-dimensional subspace of \BbbF n\times n q defines | GL r (q)| different r \times n \times n tensors.…”

Section: Comparisons and State Of The Artmentioning

confidence: 99%

See 1 more Smart Citation

Rank-Metric Codes, Semifields, and the Average Critical Problem

Anina

Ravagnani

Sheekey

et al. 2023

SIAM J. Discrete Math.

Self Cite

View full text Add to dashboard Cite

published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User

show abstract

Section: Comparisons and State Of The Artmentioning

confidence: 80%

Section: Comparisons and State Of The Artmentioning

confidence: 99%

Rank-Metric Codes, Semifields, and the Average Critical Problem

Anina

Ravagnani

Sheekey

et al. 2023

SIAM J. Discrete Math.

Self Cite

View full text Add to dashboard Cite

show abstract

Nonbinary Delsarte–goethals Codes and Finite Semifields

Rúa¹

2020

Glasgow Math. J.

View full text Add to dashboard Cite

Symplectic finite semifields can be used to construct nonlinear binary codes of Kerdock type (i.e., with the same parameters of the Kerdock codes, a subclass of Delsarte–Goethals codes). In this paper, we introduce nonbinary Delsarte–Goethals codes of parameters $(q^{m+1}\ ,\ q^{m(r+2)+2}\ ,\ {\frac{q-1}{q}(q^{m+1}-q^{\frac{m+1}{2}+r})})$ over a Galois field of order $q=2^l$ , for all $0\le r\le\frac{m-1}{2}$ , with m ≥ 3 odd, and show the connection of this construction to finite semifields.

show abstract

Binary additive MRD codes with minimum distance $$n-1$$ n - 1 must contain a semifield spread set

Cited by 2 publications

References 25 publications

Rank-Metric Codes, Semifields, and the Average Critical Problem

Rank-Metric Codes, Semifields, and the Average Critical Problem

Nonbinary Delsarte–goethals Codes and Finite Semifields

Contact Info

Product

Resources

About