[1]
|
G. N. Alfarano, M. Borello, A. Neri and A. Ravagnani, Linear cutting blocking sets and minimal codes in the rank metric, arXiv: 2106.12465.
|
[2]
|
S. Ball, The number of directions determined by a function over finite field, J. Combin. Theory Ser. A, 104 (2003), 341-350.
doi: 10.1016/j.jcta.2003.09.006.
|
[3]
|
S. Ball, A. Blokhuis, A. E. Brouwer, L. Storme and T. Szőnyi, On the number of slopes of the graph of a function defined on a finite field, J. Combin. Theory Ser. A, 86 (1999), 187-196.
doi: 10.1006/jcta.1998.2915.
|
[4]
|
D. Bartoli, B. Csajbók and M. Montanucci, On a conjecture about maximum scattered subspaces of $\mathbb{F}_{q^6} \times \mathbb{F}_{q^6}$, Linear Algebra Appl., 631 (2021), 111-135.
doi: 10.1016/j.laa.2021.08.023.
|
[5]
|
D. Bartoli, C. Zanella and F. Zullo, A new family of maximum scattered linear sets in ${\text{PG}}(1, q^6)$, Ars Math. Contemp., 19 (2020), 125-145.
doi: 10.26493/1855-3974.2137.7fa.
|
[6]
|
A. Blokhuis and M. Lavrauw, Scattered spaces with respect to a spread in ${\text{PG}}(n, q)$, Geom. Dedicata, 81 (2000), 231-243.
doi: 10.1023/A:1005283806897.
|
[7]
|
G. Bonoli and O. Polverino, $\mathbb{F}_q$-linear blocking sets in ${\text{PG}}(2, q^4)$, Innov. Incidence Geom., 2 (2005), 35-56.
doi: 10.2140/iig.2005.2.35.
|
[8]
|
A. R. Calderbank and J. M. Goethals, Three-weight codes and association schemes, Philips J. Res., 39 (1984), 143-152.
|
[9]
|
A. R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc., 18 (1986), 97-122.
doi: 10.1112/blms/18.2.97.
|
[10]
|
B. Csajbók, G. Marino and O. Polverino, Classes and equivalence of linear sets in ${\text{PG}}(1, q^n)$, J. Combin. Theory Ser. A, 157 (2018), 402-426.
doi: 10.1016/j.jcta.2018.03.007.
|
[11]
|
B. Csajbók, G. Marino and O. Polverino, A Carlitz type results for linearized polynomials, Ars Math. Contemp., 16 (2019), 585-608.
doi: 10.26493/1855-3974.1651.e79.
|
[12]
|
B. Csajbók, G. Marino, O. Polverino and C. Zanella, A new family of MRD-codes, Linear Algebra Appl., 548 (2018), 203-220.
doi: 10.1016/j.laa.2018.02.027.
|
[13]
|
B. Csajbók, G. Marino and F. Zullo, New maximum scattered linear sets of the projective line, Finite Fields Appl., 54 (2018), 133-150.
doi: 10.1016/j.ffa.2018.08.001.
|
[14]
|
J. De Beule and G. Van de Voorde, The minimum size of a linear set, J. Combin. Theory Ser. A, 164 (2019), 109-124.
doi: 10.1016/j.jcta.2018.12.008.
|
[15]
|
M. De Boeck and G. Van de Voorde, A linear set view on KM-arcs, J. Algebraic Combin., 44 (2016), 131-164.
doi: 10.1007/s10801-015-0661-7.
|
[16]
|
C. Ding and X. Wang, A coding theory construction of new systematic authentication codes, Theoret. Comput. Sci., 330 (2005), 81-99.
doi: 10.1016/j.tcs.2004.09.011.
|
[17]
|
K. Ding and C. Ding, A class of two-weight and three-weight codes and their applications in secret sharing, IEEE Trans. Inform. Theory, 61 (2015), 5835-5842.
doi: 10.1109/TIT.2015.2473861.
|
[18]
|
N. Durante, On sets with few intersection numbers in finite projective and affine spaces, Electron. J. Combin., 21 (2014), 1-18.
|
[19]
|
A. Gács and Z. Weiner, On $(q+t)$-arcs of type $(0, 2, t)$, Des. Codes Cryptogr., 29 (2003), 131-139.
doi: 10.1023/A:1024152424893.
|
[20]
|
G. Korchmáros and F. Mazzocca, On $(q+t)$-arcs of type $(0, 2, t)$ in a desarguesian plane of order $q$, Math. Proc. Camb. Philos. Soc., 108 (1990), 445-459.
doi: 10.1017/S0305004100069346.
|
[21]
|
I. N. Landjev, Linear codes over finite fields and finite projective geometries, Discrete Math., 213 (2000), 211-244.
doi: 10.1016/S0012-365X(99)00183-1.
|
[22]
|
M. Lavrauw, G. Marino, O. Polverino and R. Trombetti, Solution to an isotopism question concerning rank $2$ semifields, J. Combin. Des., 23 (2015), 60-77.
doi: 10.1002/jcd.21382.
|
[23]
|
M. Lavrauw and G. Van de Voorde, Field reduction and linear sets in finite geometry, Contemp. Math, Amer. Math. Soc., Providence, RI, 632 (2015), 271–293.
doi: 10.1090/conm/632/12633.
|
[24]
|
G. Longobardi, G. Marino, R. Trombetti and Y. Zhou, A large family of maximum scattered linear sets of ${\text{PG}}(1, q^n)$ and their associated MRD codes, arXiv: 2102.08287.
|
[25]
|
G. Longobardi and C. Zanella, Linear sets and MRD-codes arising from a class of scattered linearized polynomials, J. Algebr. Combin., 53 (2021), 639-661.
doi: 10.1007/s10801-020-01011-9.
|
[26]
|
G. Lunardon and O. Polverino, Blocking sets of size $q^t + q^{t-1} + 1$, J. Combin. Theory Ser. A, 90 (2000), 148-158.
doi: 10.1006/jcta.1999.3022.
|
[27]
|
G. Marino, M. Montanucci and F. Zullo, MRD-codes arising from the trinomial $x^q + x^{q^3}+ cx^{q^5} \in {\mathbb F}_{q^6}[x]$, Linear Algebra Appl., 591 (2020), 99-114.
doi: 10.1016/j.laa.2020.01.004.
|
[28]
|
V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, Linear sets on the projective line with complementary weights, arXiv: 2107.10641.
|
[29]
|
V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, Classifications and constructions of minimum size linear sets, submitted.
|
[30]
|
V. Napolitano and F. Zullo, Codes with few weights arising from linear sets, Adv. Math. Commun..
doi: 10.3934/amc.2020129.
|
[31]
|
A. Neri, P. Santonastaso and F. Zullo, Extending two families of maximum rank distance codes, arXiv: 2104.07602.
|
[32]
|
O. Polverino, Linear sets in finite projective spaces, Discrete Math., 310 (2010), 3096-3107.
doi: 10.1016/j.disc.2009.04.007.
|
[33]
|
O. Polverino and F. Zullo, On the number of roots of some linearized polynomials, Linear Algebra Appl., 601 (2020), 189-218.
doi: 10.1016/j.laa.2020.05.009.
|
[34]
|
J. Sheekey, A new family of linear maximum rank distance codes, Adv. Math. Commun., 10 (2016), 475-488.
doi: 10.3934/amc.2016019.
|
[35]
|
M. Shi and P. Solé, Three-weight codes, triple sum sets, and strongly walk regular graphs, Des. Codes Cryptogr., 87 (2019), 2395-2404.
doi: 10.1007/s10623-019-00628-7.
|
[36]
|
M. A. Tsfasman, S. G. Vlǎduţ and D. Nogin, Algebraic Geometric Codes: Basic Notions, Mathematical Surveys and Monographs, 139. American Mathematical Society, Providence, RI, 2007.
doi: 10.1090/surv/139.
|
[37]
|
C. Zanella and F. Zullo, Vertex properties of maximum scattered linear sets of $ {\text{PG}}(1, q^n)$, Discrete Math., 343 (2020), 111800, 14 pp.
doi: 10.1016/j.disc.2019.111800.
|
[38]
|
G. Zini and F. Zullo, Scattered subspaces and related codes, Des. Codes Cryptogr., 89 (2021), 1853-1873.
doi: 10.1007/s10623-021-00891-7.
|