On Coset Leader Graphs of Structured Linear Codes

Iceland, Eran; Samorodnitsky, Alex

doi:10.1007/s00454-019-00129-3

Cited by 2 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Discrete Bonnet-Myers theorem has recently found important applications in coding theory: it provides a completely elementary way to derive bounds on locally correctable and some locally testable binary linear codes [14].…”

Section: Introduction and Statements Of Resultsmentioning

confidence: 99%

Lin-Lu-Yau curvature and diameter of amply regular graphs

Li,

Liu

2021

Preprint

View full text Add to dashboard Cite

By Hall's marriage theorem, we study lower bounds of the Lin-Lu-Yau curvature of amply regular graphs with girth 3 or 4 under different parameter restrictions. As a consequence, we derive that the Lin-Lu-Yau curvature of any strongly regular conference graph with parameterIn general, it is still open whether the Lin-Lu-Yau curvature of an amply regular graph of parameter (n, d, α, β) with girth 3 (i.e., α ≥ 1) and β ≥ 2 is always nonnegative or not. Our approach also provides a geometric proof of a classical diameter estimates of amply regular graphs in the case of girth 4 and some special cases of girth 3.

show abstract

Section: Introduction and Statements Of Resultsmentioning

confidence: 99%

Lin-Lu-Yau curvature and diameter of amply regular graphs

Li,

Liu

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…There is an exponentially large gap between upper and lower bounds on the trade-off between code dimension and code length for -LCCs. The best known code constructions have dimension only ((log ) −1 ) (achieved by generalized Reed-Muller codes or certain lifted codes [GKS13]), whereas the best known upper bound on the dimension of -LCCs is much larger and equals ( ( −2)/( −1) ) [KT00, Woo12,IS20] . Narrowing this huge gap has remained open for over two decades.…”

Section: Introductionmentioning

confidence: 99%

Visible Rank and Codes with Locality

Alrabiah¹,

Guruswami²

2021

Preprint

View full text Add to dashboard Cite

We propose a framework to study the effect of local recovery requirements of codeword symbols on the dimension of linear codes, based on a combinatorial proxy that we call visible rank. The locality constraints of a linear code are stipulated by a matrix of ★'s and 0's (which we call a "stencil"), whose rows correspond to the local parity checks (with the ★'s indicating the support of the check). The visible rank of is the largest for which there is a × submatrix in with a unique generalized diagonal of ★'s. The visible rank yields a field-independent combinatorial lower bound on the rank of and thus the co-dimension of the code.

show abstract

On Coset Leader Graphs of Structured Linear Codes

Cited by 2 publications

References 20 publications

Lin-Lu-Yau curvature and diameter of amply regular graphs

Lin-Lu-Yau curvature and diameter of amply regular graphs

Visible Rank and Codes with Locality

Contact Info

Product

Resources

About