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On codes over rings invariant under affine groups
The classification of complementary information set codes of lengths $14$ and $16$
1. | Department of Mathematics, Ohio Dominican University, 1216 Sunbury Road, Columbus, OH 43219, United States |
References:
[1] |
K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, Des. Codes Crypt., 23 (2001), 11-21.
doi: 10.1023/A:1011203416769. |
[2] |
K. Betsumiya and M. Harada, Classification of formally self-dual even codes of lengths up to 16, Des. Codes Crypt., 23 (2001), 325-332.
doi: 10.1023/A:1011223128089. |
[3] |
K. Betsumiya, M. Harada and A. Munemasa, A complete classification of doubly-even self-dual codes of length 40, preprint, arXiv:1104.3727v2 |
[4] |
J. Cannon and C. Playoust, "An Introduction to Magma,'' University of Sydney, Sydney, Australia, 1994. |
[5] |
C. Carlet, P. Gaborit, J.-L. Kim and P. Solé, A new class of codes for Boolean masking of cryptographic computations, preprint, arXiv:1110.1193v2
doi: 10.1109/TIT.2012.2200651. |
[6] |
I. A. Faradzev, Constructive enumeration of combinatorial objects, in "Problemes Combinatoires et Theorie des Graphes Colloque Internat,'' CNRS, Paris, (1978), 131-135. |
[7] |
J. E. Fields, P. Gaborit, W. C. Huffman and V. Pless, On the classification of extremal even formally self-dual codes of lengths 20 and 22, Discrete Appl. Math., 111 (2001), 75-86.
doi: 10.1016/S0166-218X(00)00345-0. |
[8] |
F. Freibert, A classification of binary [16,8,4] codes; A classification of [14,7] CIS codes, available online at http://finleyfreibert.wordpress.com/mathematics-research/, 2012. |
[9] |
T. A. Gulliver and P. R. J. Östergard, Binary optimal linear rate 1/2 codes, Discrete Math., 283 (2004), 255-261.
doi: 10.1016/j.disc.2003.10.027. |
[10] |
S. Han, H. Lee and Y. Lee, Binary formally self-dual odd codes, Des. Codes Crypt., 61 (2010), 141-150.
doi: 10.1007/s10623-010-9444-2. |
[11] |
W. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge University Press, Cambridge, 2003. |
[12] |
P. Kaski and P. R. J. Östergard, "Classification Algorithms for Codes and Designs,'' Springer, Berlin, 2006. |
[13] |
H. Maghrebi, C. Carlet, S. Guilley and J.-L. Danger, Optimal first-order masking with linear and non-linear bijections, in "Progress in Cryptology - AFRICACRYPT 2012,'' (2012), 360-377.
doi: 10.1007/978-3-642-31410-0_22. |
[14] |
H. Maghrebi, S. Guilley, C. Carlet and J.-L. Danger, Classification of high-order Boolean masking Schemes and improvements of their efficiency, available online at http://eprint.iacr.org/2011/520.pdf, 2011. |
[15] |
H. Maghrebi, S. Guilley and J.-L. Danger, Leakage squeezing countermeasure against high-order attacks, in "Information Security Theory and Practice,'' Springer, Berlin, (2011), 208-223.
doi: 10.1007/978-3-642-21040-2_14. |
[16] |
B. D. McKay, Nauty user's guide (version 2.4), available online at http://cs.anu.edu.au/~bdm/nauty/nug.pdf, 2009. |
[17] |
P. R. J. Östergard, Classifying subspaces of hamming spaces, Des. Codes Crypt., 27 (2000), 297-305.
doi: 10.1023/A:1019903407222. |
[18] |
V. Pless, A classification of self-orthogonal codes over $GF(2)$, Discrete Math., 3 (1972), 215-228.
doi: 10.1016/0012-365X(72)90034-9. |
[19] |
R. C. Read, Every one a winner; or, how to avoid isomorphism search when cataloguing combinatorial configurations, Ann. Discrete Math., 2 (1978), 107-120.
doi: 10.1016/S0167-5060(08)70325-X. |
[20] |
M. Rivain and E. Prouff, Provably secure higher-order masking of AES, in "Cryptographic Hardware and Embedded Systems, CHES 2010,'' Springer, Berlin, (2010), 413-427.
doi: 10.1007/978-3-642-15031-9_28. |
[21] |
H. G. Schaathun, On higher weights and code existence, in "Cryptography and Coding,'' Springer, Berlin, (2009), 56-64.
doi: 10.1007/978-3-642-10868-6_4. |
[22] |
J. Simonis, A description of the $[16,7,6]$ codes, in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes,'' Springer, Berlin, (1991), 25-35.
doi: 10.1007/3-540-54195-0_36. |
show all references
References:
[1] |
K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, Des. Codes Crypt., 23 (2001), 11-21.
doi: 10.1023/A:1011203416769. |
[2] |
K. Betsumiya and M. Harada, Classification of formally self-dual even codes of lengths up to 16, Des. Codes Crypt., 23 (2001), 325-332.
doi: 10.1023/A:1011223128089. |
[3] |
K. Betsumiya, M. Harada and A. Munemasa, A complete classification of doubly-even self-dual codes of length 40, preprint, arXiv:1104.3727v2 |
[4] |
J. Cannon and C. Playoust, "An Introduction to Magma,'' University of Sydney, Sydney, Australia, 1994. |
[5] |
C. Carlet, P. Gaborit, J.-L. Kim and P. Solé, A new class of codes for Boolean masking of cryptographic computations, preprint, arXiv:1110.1193v2
doi: 10.1109/TIT.2012.2200651. |
[6] |
I. A. Faradzev, Constructive enumeration of combinatorial objects, in "Problemes Combinatoires et Theorie des Graphes Colloque Internat,'' CNRS, Paris, (1978), 131-135. |
[7] |
J. E. Fields, P. Gaborit, W. C. Huffman and V. Pless, On the classification of extremal even formally self-dual codes of lengths 20 and 22, Discrete Appl. Math., 111 (2001), 75-86.
doi: 10.1016/S0166-218X(00)00345-0. |
[8] |
F. Freibert, A classification of binary [16,8,4] codes; A classification of [14,7] CIS codes, available online at http://finleyfreibert.wordpress.com/mathematics-research/, 2012. |
[9] |
T. A. Gulliver and P. R. J. Östergard, Binary optimal linear rate 1/2 codes, Discrete Math., 283 (2004), 255-261.
doi: 10.1016/j.disc.2003.10.027. |
[10] |
S. Han, H. Lee and Y. Lee, Binary formally self-dual odd codes, Des. Codes Crypt., 61 (2010), 141-150.
doi: 10.1007/s10623-010-9444-2. |
[11] |
W. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes,'' Cambridge University Press, Cambridge, 2003. |
[12] |
P. Kaski and P. R. J. Östergard, "Classification Algorithms for Codes and Designs,'' Springer, Berlin, 2006. |
[13] |
H. Maghrebi, C. Carlet, S. Guilley and J.-L. Danger, Optimal first-order masking with linear and non-linear bijections, in "Progress in Cryptology - AFRICACRYPT 2012,'' (2012), 360-377.
doi: 10.1007/978-3-642-31410-0_22. |
[14] |
H. Maghrebi, S. Guilley, C. Carlet and J.-L. Danger, Classification of high-order Boolean masking Schemes and improvements of their efficiency, available online at http://eprint.iacr.org/2011/520.pdf, 2011. |
[15] |
H. Maghrebi, S. Guilley and J.-L. Danger, Leakage squeezing countermeasure against high-order attacks, in "Information Security Theory and Practice,'' Springer, Berlin, (2011), 208-223.
doi: 10.1007/978-3-642-21040-2_14. |
[16] |
B. D. McKay, Nauty user's guide (version 2.4), available online at http://cs.anu.edu.au/~bdm/nauty/nug.pdf, 2009. |
[17] |
P. R. J. Östergard, Classifying subspaces of hamming spaces, Des. Codes Crypt., 27 (2000), 297-305.
doi: 10.1023/A:1019903407222. |
[18] |
V. Pless, A classification of self-orthogonal codes over $GF(2)$, Discrete Math., 3 (1972), 215-228.
doi: 10.1016/0012-365X(72)90034-9. |
[19] |
R. C. Read, Every one a winner; or, how to avoid isomorphism search when cataloguing combinatorial configurations, Ann. Discrete Math., 2 (1978), 107-120.
doi: 10.1016/S0167-5060(08)70325-X. |
[20] |
M. Rivain and E. Prouff, Provably secure higher-order masking of AES, in "Cryptographic Hardware and Embedded Systems, CHES 2010,'' Springer, Berlin, (2010), 413-427.
doi: 10.1007/978-3-642-15031-9_28. |
[21] |
H. G. Schaathun, On higher weights and code existence, in "Cryptography and Coding,'' Springer, Berlin, (2009), 56-64.
doi: 10.1007/978-3-642-10868-6_4. |
[22] |
J. Simonis, A description of the $[16,7,6]$ codes, in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes,'' Springer, Berlin, (1991), 25-35.
doi: 10.1007/3-540-54195-0_36. |
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