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Add skew Hadamard matrices up to order 1000 #35211

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c0eb0c1
SDS functions return also the group from which sets are generated
MatteoCati Feb 7, 2023
7f30eef
Improve is_supplementary_difference_set, fix bug when lambda=0
MatteoCati Feb 12, 2023
5c45baf
Add is_complementary_difference_set function
MatteoCati Feb 12, 2023
f777090
Add first construction for complementary difference sets
MatteoCati Feb 12, 2023
f68b661
Rename is_complementary_difference_set to plural
MatteoCati Feb 13, 2023
270396c
Add second construction for complementary difference sets
MatteoCati Feb 14, 2023
6b3a5a9
change return type of complementary_difference_setI
MatteoCati Feb 14, 2023
876236f
Add third construction of complementary difference sets
MatteoCati Feb 14, 2023
a53394c
Add general construction of complementary difference sets
MatteoCati Feb 14, 2023
5186102
Add SEEALSO blocks
MatteoCati Feb 14, 2023
622c3fe
Add Spence construction for skew Hadamard matrix
MatteoCati Feb 14, 2023
e96b9d6
Add spence construction to skew_hadamard_matrix
MatteoCati Feb 14, 2023
3dd63fc
Add construction of skew SDS over polynomial ring
MatteoCati Feb 14, 2023
b0f4599
skew_supplementary_difference_set function uses also construction fro…
MatteoCati Feb 14, 2023
a7b8665
GS_skew_hadamard_smallcases work even if SDS are from polynomial ring
MatteoCati Feb 14, 2023
6d558bd
Remove skew_hadamard_matrix_324 (it is now implemented using the skew…
MatteoCati Feb 14, 2023
c4e749e
Add SDS of order 213, 251, 631
MatteoCati Feb 15, 2023
6506ce0
Add construction of skew SDS of order 239 with Paley-Todd difference set
MatteoCati Feb 15, 2023
f852f0f
Add skew SDS of order 331
MatteoCati Feb 15, 2023
f505f51
Add link to new skew SDS function
MatteoCati Feb 15, 2023
effeb87
Fix complementary difference sets existence conditions
MatteoCati Feb 17, 2023
6e502a2
Fix spence skew_hadamard_matrix_spence_1975 existence conditions
MatteoCati Feb 17, 2023
e1bf711
use plural name for complementary_difference_sets functions
MatteoCati Feb 21, 2023
225d6ea
Add complementary difference sets to difference_family function
MatteoCati Feb 24, 2023
36d348a
Add function for checking amicable Hadamard matrices
MatteoCati Feb 26, 2023
661bdb2
Add construction for amicable Hadamard matrices of order q+1
MatteoCati Feb 26, 2023
d5d1a37
Add general construction for amicable Hadamard matrices
MatteoCati Feb 26, 2023
60c1f0f
Add construction for skew Hadamard matrices from OD
MatteoCati Feb 26, 2023
bebeec2
Change Spe1975 reference to avoid clash
MatteoCati Feb 27, 2023
b7f29ec
Move Spe1975 to correct alphabetical position in reference file
MatteoCati Feb 27, 2023
2bc9a49
Fix docstring
MatteoCati Feb 27, 2023
9b6d926
Merge branch 'develop' into add_skew_hadamard_matrices_up_to_1000
MatteoCati Mar 4, 2023
9a736c5
Replace Whiteman construction with more general one
MatteoCati Mar 8, 2023
c0e4360
Fix bug in construction of SDS from relative difference sets
MatteoCati Mar 8, 2023
d52e647
Merge branch 'develop' into add_skew_hadamard_matrices_up_to_1000
MatteoCati Mar 13, 2023
0989b45
Add info about orders covered in the documentation
MatteoCati Mar 14, 2023
a71b10d
Add optional parameter for returning group
MatteoCati Mar 15, 2023
6d0d29b
Make is_supplementary_difference_set backwards compatible
MatteoCati Mar 15, 2023
eb3dc78
Make renaming of supplementary_difference_set_from_rel_diff_set backw…
MatteoCati Mar 15, 2023
71a069a
Merge branch 'develop' into add_skew_hadamard_matrices_up_to_1000
MatteoCati Mar 22, 2023
dbe24a6
Fix docs in hadamard_matrix.py
MatteoCati Mar 22, 2023
0826ce7
Change ValueError to NotImplementedError
MatteoCati Mar 23, 2023
375b5e5
fix docs in difference_family.py
MatteoCati Mar 23, 2023
c6db754
fix error messages in difference_family.py
MatteoCati Mar 23, 2023
df5dffa
Use list comprehensions instead of map
MatteoCati Mar 23, 2023
7ac2641
Add function for checking all Hadamard matrices
MatteoCati Mar 23, 2023
c4abaaf
Fix docstring of _get_all_hadamard_matrices
MatteoCati Mar 23, 2023
0bacdb2
Move tests to file header
MatteoCati Mar 27, 2023
1c45544
Merge branch 'develop' into add_skew_hadamard_matrices_up_to_1000
MatteoCati Mar 27, 2023
f1e5033
Add explanation for test
MatteoCati Mar 27, 2023
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40 changes: 35 additions & 5 deletions src/doc/en/reference/references/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -2018,6 +2018,11 @@ REFERENCES:
Lexicographically: an efficient new strategy compared with others, 2020,
https://hal.archives-ouvertes.fr/hal-02462764v1

.. [DGK2014] \D. Đoković, O. Golubitsky and I.Kotsireas.
*Some New Orders of Hadamard and Skew-Hadamard Matrices*,
Journal of Combinatorial Designs 22(6) (2014): 270-277.
:doi:`10.1002/jcd.21358`

.. [DGMPPS2019] \N. Datta, A. Ghoshal, D. Mukhopadhyay, S. Patranabis,
S. Picek, R. Sashukhan. "TRIFLE"
https://csrc.nist.gov/CSRC/media/Projects/Lightweight-Cryptography/documents/round-1/spec-doc/trifle-spec.pdf
Expand Down Expand Up @@ -2105,6 +2110,12 @@ REFERENCES:
.. [DK2013] John R. Doyle and David Krumm, *Computing algebraic
numbers of bounded height*, :arxiv:`1111.4963v4` (2013).

.. [DK2016] \D. Ðokovic, I. Kotsireas.
*A class of cyclic (v; k1, k2, k3; λ) difference families
with v = 3 (mod 4) a prime*,
Special Matrices 4(1) (2016): 317-325.
:doi:`10.1515/spma-2016-0029`

.. [DLHK2007] \J. A. De Loera, D. C. Haws, M. Köppe, Ehrhart
polynomials of matroid polytopes and
polymatroids. Discrete & Computational Geometry, Volume
Expand Down Expand Up @@ -5431,6 +5442,10 @@ REFERENCES:
*Wide-open encryption design offers flexible implementations*; in
Cryptologia, (1985), pp. 75-91.

.. [Seb1978] \J. Seberry.
*On Skew Hadamard Matrices*,
Ars Combinatoria 6 (1978): 255-276.

.. [Seb2017] \J. Seberry,
*Orthogonal designs: Hadamard matrices, quadratic forms and algebras*.
Springer 2017. :doi:`10.1007/978-3-319-59032-5`
Expand Down Expand Up @@ -5579,6 +5594,16 @@ REFERENCES:
:doi:`10.1007/978-1-4684-9322-1`,
ISBN 978-1-4684-9322-1.

.. [Spe1975] \E. Spence.
*Hadamard matrices from relative difference sets*,
Journal of Combinatorial Theory, Series A 19(3) (1975): 287-300.
:doi:`10.1016/0097-3165(75)90054-0`

.. [Spe1975b] \E. Spence.
*Skew-Hadamard Matrices of the Goethals-Seidel Type*,
Canadian Journal of Mathematics 27(3) (1975): 555-560.
:doi:`10.4153/cjm-1975-066-9`

.. [Spe1977] \E. Spence.
*Skew-Hadamard matrices of order 2(q + 1)*,
Discrete Mathematics 18(1) (1977): 79-85.
Expand Down Expand Up @@ -5724,11 +5749,6 @@ REFERENCES:
matrices, and characteristic polynomials without division*
:doi:`10.1023/A:1021878507303`

.. [Spe1975] \E. Spence.
*Hadamard matrices from relative difference sets*,
Journal of Combinatorial Theory, Series A 19(3) (1975): 287-300.
:doi:`10.1016/0097-3165(75)90054-0`

.. [ST1981] \J. J. Seidel and D. E. Taylor,
*Two-graphs, a second survey*.
Algebraic methods in graph theory, Vol. I, II (Szeged, 1978),
Expand Down Expand Up @@ -5933,6 +5953,11 @@ REFERENCES:
Hall-Littlewood vertex operators and generalized Kostka polynomials.
Adv. Math. 158 (2001), no. 1, 66-85.

.. [Sze1971] \G. Szekeres.
*Cyclotomy and complementary difference sets*,
Acta Arithmetica 18 (1971): 349-353.
:doi:`10.4064/aa-18-1-349-353`

.. [Sze1988] \G. Szekeres.
*A note on skew type orthogonal ±1 matrices*,
Combinatorics, Colloquia Mathematica Societatis, Janos Bolyai, 52 (1988): 489-498.
Expand Down Expand Up @@ -6151,6 +6176,11 @@ REFERENCES:
.. [Wal1970] David W. Walkup, "The lower bound conjecture for 3- and
4-manifolds", Acta Math. 125 (1970), 75-107.

.. [Wal1970b] \J. Wallis.
*(v, k, λ) Configurations and Hadamard matrices*,
Journal of the Australian Mathematical Society 11(3) (1970): 297-309.
:doi:`10.1017/S1446788700006674`

.. [Wal2001] Timothy Walsh, *Gray codes for involutions*, J. Combin.
Math. Combin. Comput. **36** (2001), 95-118.
http://www.info2.uqam.ca/~walsh_t/papers/Involutions%20paper.pdf
Expand Down
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