Revised : 2018-05-16

Accepted : 2018-05-19

Published online : 2019-02-04

DOI : https://doi.org/10.5802/alco.22

Classification: 05E30

Keywords: association schemes, symmetric designs

@article{ALCO_2019__2_1_119_0, author = {Kodalen, Brian G.}, title = {Linked systems of symmetric designs}, journal = {Algebraic Combinatorics}, publisher = {MathOA foundation}, volume = {2}, number = {1}, year = {2019}, pages = {119-147}, doi = {10.5802/alco.22}, language = {en}, url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_1_119_0} }

Kodalen, Brian G. Linked systems of symmetric designs. Algebraic Combinatorics, Volume 2 (2019) no. 1, pp. 119-147. doi : 10.5802/alco.22. https://alco.centre-mersenne.org/item/ALCO_2019__2_1_119_0/

[1] On Boolean functions with the sum of every two of them being bent, Des. Codes Cryptography, Volume 49 (2008) no. 1-3, pp. 341-346 | Article | MR 2438460 | Zbl 1196.05010

[2] Distance-regular graphs, Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., Volume 18 (1989), xviii+495 pages | Article | MR 1002568 | Zbl 0747.05073

[3] On groups with several doubly-transitive permutation representations, Math. Z., Volume 128 (1972), pp. 1-14 | Article | MR 0316538 | Zbl 0227.20001

[4] Quadratic forms over $GF\left(2\right)$, Nederl. Akad. Wet., Proc., Ser. A, Volume 76 (1973), pp. 1-8 | MR 0327801 | Zbl 0258.05022

[5] Handbook of combinatorial designs, Chapman & Hall/CRC, Discrete Mathematics and its Applications (2007), xxii+984 pages | MR 2246267 | Zbl 1101.05001

[6] Linking systems in nonelementary abelian groups, J. Comb. Theory, Ser. A, Volume 123 (2014), pp. 92-103 | Article | MR 3157802 | Zbl 1281.05131

[7] Large equiangular sets of lines in Euclidean space, Electron. J. Comb., Volume 7 (2000), R55, 3 pages http://www.combinatorics.org/volume_7/abstracts/v7i1r55.html | MR 1795615 | Zbl 0966.51010

[8] Nonlinear codes defined by quadratic forms over $\mathrm{GF}\left(2\right)$, Inform. and Control, Volume 31 (1976) no. 1, pp. 43-74 | Article | MR 0406682 | Zbl 0337.94007

[9] On the real unbiased Hadamard matrices, Combinatorics and graphs, American Mathematical Society (Contemporary Mathematics) Volume 531 (2010), pp. 243-250 | Article | MR 2757803 | Zbl 1231.05043

[10] Kirkman equiangular tight frames and codes, IEEE Trans. Inf. Theory, Volume 60 (2014) no. 1, pp. 170-181 | Article | MR 3150919 | Zbl 1364.42036

[11] Linking systems of difference sets (2017) (https://arxiv.org/abs/1708.04405 )

[12] Euler squares, Ann. Math., Volume 23 (1922) no. 3, pp. 221-227 | Article | MR 1502613

[13] Imprimitive cometric association schemes: constructions and analysis, J. Algebr. Comb., Volume 25 (2007) no. 4, pp. 399-415 | Article | MR 2320370 | Zbl 1118.05100

[14] The systems of linked $2$-$(16,\phantom{\rule{0.166667em}{0ex}}6,\phantom{\rule{0.166667em}{0ex}}2)$ designs, Ars Comb., Volume 11 (1981), pp. 131-148 | MR 629867 | Zbl 0468.05012

[15] Symmetric Bush-type Hadamard matrices of order $4{m}^{4}$ exist for all odd $m$, Proc. Am. Math. Soc., Volume 134 (2006) no. 8, pp. 2197-2204 | Article | MR 2213691 | Zbl 1088.05020

[16] On homogeneous systems of linked symmetric designs, Math. Z., Volume 138 (1974), pp. 15-20 | Article | MR 0347636 | Zbl 0275.05016

[17] Coherent configurations and triply regular association schemes obtained from spherical designs, J. Comb. Theory, Ser. A, Volume 117 (2010) no. 8, pp. 1178-1194 | Article | MR 2677683 | Zbl 1206.05105

[18] An Asymptotic Existence Theory on Incomplete Mutually Orthogonal Latin Squares. (2015) (master thesis, University of Victoria (Canada))

[19] Three-class association schemes, J. Algebr. Comb., Volume 10 (1999) no. 1, pp. 69-107 | Article | MR 1701285 | Zbl 0929.05096

[20] Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems, J. Comb. Theory, Ser. A, Volume 120 (2013) no. 7, pp. 1401-1439 | Article | MR 3092674 | Zbl 1314.05236

[21] Introduction to coding theory, Springer, Graduate Texts in Mathematics, Volume 86 (1999), xiv+227 pages | Article | MR 1664228

[22] New construction of mutually unbiased bases in square dimensions, Quantum Inf. Comput., Volume 5 (2005) no. 2, pp. 93-101 | MR 2132048 | Zbl 1213.81108