Constructions and families of covering codes and saturated sets of points in projective geometry

DOI10.1109/18.476339zbMath0845.94022OpenAlexW2079279879MaRDI QIDQ4880341

Alexander A. Davydov

Publication date: 15 September 1996

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/18.476339

zbMATH Keywords

covering radiuscovering codesprojective geometriessaturated sets

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Combinatorial aspects of finite geometries (05B25) Combinatorial codes (94B25) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75) Combinatorial aspects of packing and covering (05B40)

Related Items (14)

On the resilience of Even-Mansour to invariant permutations ⋮ Further results on multiple coverings of the farthest-off points ⋮ Constructing saturating sets in projective spaces using subgeometries ⋮ Ternary covering codes derived from BCH codes ⋮ On saturating sets in projective spaces. ⋮ Upper bounds on the length function for covering codes with covering radius \(R\) and codimension \(tR+1\) ⋮ Saturating systems and the rank-metric covering radius ⋮ Galois geometries and coding theory ⋮ On the minimum size of complete arcs and minimal saturating sets in projective planes ⋮ Linear codes with covering radius 3 ⋮ Multiple coverings of the farthest-off points with small density from projective geometry ⋮ New quaternary linear codes with covering radius 2 ⋮ On saturating sets in small projective geometries ⋮ New covering codes of radius \(R\), codimension \(tr\) and \(tr+\frac{R}{2}\), and saturating sets in projective spaces

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