New bounds for linear codes of covering radii 2 and 3

Author:

Bartoli Daniele,Davydov Alexander A.ORCID,Giulietti Massimo,Marcugini Stefano,Pambianco Fernanda

Funder

Ministry for Education, University and Research of Italy

Italian National Group for Algebraic and Geometric Structures and their Applications

Russian Foundation for Sciences

University of Perugia

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Theory and Mathematics,Computer Networks and Communications

Reference32 articles.

1. Bartoli, D., Davydov, A.A., Faina, G., Kreshchuk, A.A., Marcugini, S., Pambianco, F.: Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane PG(2, q) for all q ≤ 160001 and sporadic q in the interval [160801…430007]. arXiv: 1312.2155v3 (2015)

2. Bartoli, D., Davydov, A.A., Faina, G., Kreshchuk, A.A., Marcugini, S., Pambianco, F.: Tables, bounds and graphics of sizes of complete lexiarcs in the plane PG(2, q) for all q ≤ 301813 and sporadic q in the interval [301897…430007] obtained by an algorithm with fixed order of points (FOP). arXiv: 1404.0469v2 (2015)

3. Bartoli, D., Davydov, A.A., Faina, G., Kreshchuk, A.A., Marcugini, S., Pambianco, F.: Upper bounds on the smallest size of a complete arc in a finite Desarguesian projective plane based on computer search. J. Geometry 107(1), 89–117 (2016)

4. Bartoli, D., Davydov, A.A., Faina, G., Kreshchuk, A.A., Marcugini, S., Pambianco, F.: Tables, bounds and graphics of sizes of complete arcs in the plane PG(2, q) for all q ≤ 321007 and sporadic q in [323761…430007] obtained by an algorithm with fixed order of points (FOP). arXiv: 1404.0469v3 (2018)

5. Bartoli, D., Davydov, A.A., Giulietti, M., Marcugini, S., Pambianco, F.: On upper bounds on the smallest size of a saturating set in a projective plane. arXiv: 1505.01426 (2015)

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1. Upper bounds on the length function for covering codes with covering radius $ R $ and codimension $ tR+1 $;Advances in Mathematics of Communications;2023

2. New bounds for covering codes of radius 3 and codimension $ 3t+1 $;Advances in Mathematics of Communications;2023

3. Constructing saturating sets in projective spaces using subgeometries;Designs, Codes and Cryptography;2021-10-24

4. Bounds for Complete Arcs in $$\mathrm {PG}(3,q)$$ and Covering Codes of Radius 3, Codimension 4, Under a Certain Probabilistic Conjecture;Computational Science and Its Applications – ICCSA 2020;2020

5. New bounds for linear codes of covering radius 3 and 2-saturating sets in projective spaces;2019 XVI International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY);2019-10

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