-
Previous Article
Discrete logarithm like problems and linear recurring sequences
- AMC Home
- This Issue
-
Next Article
Self-orthogonal codes from orbit matrices of 2-designs
A new class of majority-logic decodable codes derived from polarity designs
1. | Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, United States, United States |
References:
[1] |
E. F. Assmus Jr. and J. D. Key, "Designs and Their Codes,'' Cambridge Univ. Press, Cambridge, 1992. |
[2] |
T. Beth, D. Jungnickel and H. Lenz, "Design Theory,'' 2nd edition, Cambridge Univ. Press, Cambridge, 1999. |
[3] |
I. F. Blake and R. C. Mullin, "The Mathematical Theory of Coding,'' Academic Press, New York, 1975. |
[4] |
D. Clark, D. Jungnickel and V. D. Tonchev, Affine geometry designs, polarities, and Hamada's conjecture, J. Combin. Theory Ser. A, 118 (2011), 231-239.
doi: 10.1016/j.jcta.2010.06.007. |
[5] |
P. Delsarte, J.-M. Goethals and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Inform. Control, 16 (1970), 403-442.
doi: 10.1016/S0019-9958(70)90214-7. |
[6] |
J.-M. Goethals and P. Delsarte, On a class of majority-decodable cyclic codes, IEEE Trans. Inform. Theory, 14 (1968), 182-188. |
[7] |
N. Hamada, On the $p$-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its application to error correcting codes, Hiroshima Math. J., 3 (1973), 154-226. |
[8] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, Oxford Univ. Press, Oxford, 1988. |
[9] |
D. Jungnickel and V. D. Tonchev, Polarities, quasi-symmetric designs, and Hamada's conjecture, Des. Codes Cryptogr., 51 (2009), 131-140.
doi: 10.1007/s10623-008-9249-8. |
[10] |
D. Jungnickel and V. D. Tonchev, The number of designs with geometric parameters grows exponentially, Des. Codes Cryptogr., 55 (2010), 131-140.
doi: 10.1007/s10623-009-9299-6. |
[11] |
D. E. Muller, Application of Boolean algebra to switching circuit design and to error detection, IRE Trans. Electron. Comput., EC-3 (1954), 6-12. |
[12] |
W. W. Peterson and E. J. Weldon, "Error-Correcting Codes,'' 2nd edition, MIT Press, Cambridge, MA, 1972. |
[13] |
M. Rahman and I. F. Blake, Majority logic decoding using combinatorial designs, IEEE Trans. Inform. Theory, 21 (1975), 585-587.
doi: 10.1109/TIT.1975.1055428. |
[14] |
I. S. Reed, A class of multiple-error correcting codes and the decoding scheme, IRE Trans. Inform. Theory, 4 (1954), 38-49. |
[15] |
L. D. Rudolph, A class of majority logic decodable codes, IEEE Trans. Inform. Theory, 13 (1967), 305-307.
doi: 10.1109/TIT.1967.1053994. |
[16] |
V. D. Tonchev, "Combinatorial Configurations: Designs, Codes, Graphs,'' Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1988. |
[17] |
E. J. Weldon, Euclidean geometry cyclic codes, in "Proceedings of the Conference on Combinatorial Mathematics and its Applications,'' Univ. North Carolina, Chapel Hill, 1967. |
show all references
References:
[1] |
E. F. Assmus Jr. and J. D. Key, "Designs and Their Codes,'' Cambridge Univ. Press, Cambridge, 1992. |
[2] |
T. Beth, D. Jungnickel and H. Lenz, "Design Theory,'' 2nd edition, Cambridge Univ. Press, Cambridge, 1999. |
[3] |
I. F. Blake and R. C. Mullin, "The Mathematical Theory of Coding,'' Academic Press, New York, 1975. |
[4] |
D. Clark, D. Jungnickel and V. D. Tonchev, Affine geometry designs, polarities, and Hamada's conjecture, J. Combin. Theory Ser. A, 118 (2011), 231-239.
doi: 10.1016/j.jcta.2010.06.007. |
[5] |
P. Delsarte, J.-M. Goethals and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Inform. Control, 16 (1970), 403-442.
doi: 10.1016/S0019-9958(70)90214-7. |
[6] |
J.-M. Goethals and P. Delsarte, On a class of majority-decodable cyclic codes, IEEE Trans. Inform. Theory, 14 (1968), 182-188. |
[7] |
N. Hamada, On the $p$-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its application to error correcting codes, Hiroshima Math. J., 3 (1973), 154-226. |
[8] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, Oxford Univ. Press, Oxford, 1988. |
[9] |
D. Jungnickel and V. D. Tonchev, Polarities, quasi-symmetric designs, and Hamada's conjecture, Des. Codes Cryptogr., 51 (2009), 131-140.
doi: 10.1007/s10623-008-9249-8. |
[10] |
D. Jungnickel and V. D. Tonchev, The number of designs with geometric parameters grows exponentially, Des. Codes Cryptogr., 55 (2010), 131-140.
doi: 10.1007/s10623-009-9299-6. |
[11] |
D. E. Muller, Application of Boolean algebra to switching circuit design and to error detection, IRE Trans. Electron. Comput., EC-3 (1954), 6-12. |
[12] |
W. W. Peterson and E. J. Weldon, "Error-Correcting Codes,'' 2nd edition, MIT Press, Cambridge, MA, 1972. |
[13] |
M. Rahman and I. F. Blake, Majority logic decoding using combinatorial designs, IEEE Trans. Inform. Theory, 21 (1975), 585-587.
doi: 10.1109/TIT.1975.1055428. |
[14] |
I. S. Reed, A class of multiple-error correcting codes and the decoding scheme, IRE Trans. Inform. Theory, 4 (1954), 38-49. |
[15] |
L. D. Rudolph, A class of majority logic decodable codes, IEEE Trans. Inform. Theory, 13 (1967), 305-307.
doi: 10.1109/TIT.1967.1053994. |
[16] |
V. D. Tonchev, "Combinatorial Configurations: Designs, Codes, Graphs,'' Longman Scientific & Technical, Harlow; John Wiley & Sons, Inc., New York, 1988. |
[17] |
E. J. Weldon, Euclidean geometry cyclic codes, in "Proceedings of the Conference on Combinatorial Mathematics and its Applications,'' Univ. North Carolina, Chapel Hill, 1967. |
[1] |
Martino Borello, Olivier Mila. Symmetries of weight enumerators and applications to Reed-Muller codes. Advances in Mathematics of Communications, 2019, 13 (2) : 313-328. doi: 10.3934/amc.2019021 |
[2] |
Daniele Bartoli, Adnen Sboui, Leo Storme. Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes. Advances in Mathematics of Communications, 2016, 10 (2) : 355-365. doi: 10.3934/amc.2016010 |
[3] |
Olav Geil, Stefano Martin. Relative generalized Hamming weights of q-ary Reed-Muller codes. Advances in Mathematics of Communications, 2017, 11 (3) : 503-531. doi: 10.3934/amc.2017041 |
[4] |
Andreas Klein, Leo Storme. On the non-minimality of the largest weight codewords in the binary Reed-Muller codes. Advances in Mathematics of Communications, 2011, 5 (2) : 333-337. doi: 10.3934/amc.2011.5.333 |
[5] |
Johan Rosenkilde. Power decoding Reed-Solomon codes up to the Johnson radius. Advances in Mathematics of Communications, 2018, 12 (1) : 81-106. doi: 10.3934/amc.2018005 |
[6] |
Crnković Dean, Vedrana Mikulić Crnković, Bernardo G. Rodrigues. On self-orthogonal designs and codes related to Held's simple group. Advances in Mathematics of Communications, 2018, 12 (3) : 607-628. doi: 10.3934/amc.2018036 |
[7] |
Kwankyu Lee. Decoding of differential AG codes. Advances in Mathematics of Communications, 2016, 10 (2) : 307-319. doi: 10.3934/amc.2016007 |
[8] |
Elisa Gorla, Felice Manganiello, Joachim Rosenthal. An algebraic approach for decoding spread codes. Advances in Mathematics of Communications, 2012, 6 (4) : 443-466. doi: 10.3934/amc.2012.6.443 |
[9] |
Washiela Fish, Jennifer D. Key, Eric Mwambene. Partial permutation decoding for simplex codes. Advances in Mathematics of Communications, 2012, 6 (4) : 505-516. doi: 10.3934/amc.2012.6.505 |
[10] |
Alexander Barg, Arya Mazumdar, Gilles Zémor. Weight distribution and decoding of codes on hypergraphs. Advances in Mathematics of Communications, 2008, 2 (4) : 433-450. doi: 10.3934/amc.2008.2.433 |
[11] |
Yujuan Li, Guizhen Zhu. On the error distance of extended Reed-Solomon codes. Advances in Mathematics of Communications, 2016, 10 (2) : 413-427. doi: 10.3934/amc.2016015 |
[12] |
Peter Beelen, David Glynn, Tom Høholdt, Krishna Kaipa. Counting generalized Reed-Solomon codes. Advances in Mathematics of Communications, 2017, 11 (4) : 777-790. doi: 10.3934/amc.2017057 |
[13] |
Antonio Cafure, Guillermo Matera, Melina Privitelli. Singularities of symmetric hypersurfaces and Reed-Solomon codes. Advances in Mathematics of Communications, 2012, 6 (1) : 69-94. doi: 10.3934/amc.2012.6.69 |
[14] |
Uri Shapira. On a generalization of Littlewood's conjecture. Journal of Modern Dynamics, 2009, 3 (3) : 457-477. doi: 10.3934/jmd.2009.3.457 |
[15] |
Terasan Niyomsataya, Ali Miri, Monica Nevins. Decoding affine reflection group codes with trellises. Advances in Mathematics of Communications, 2012, 6 (4) : 385-400. doi: 10.3934/amc.2012.6.385 |
[16] |
Heide Gluesing-Luerssen, Uwe Helmke, José Ignacio Iglesias Curto. Algebraic decoding for doubly cyclic convolutional codes. Advances in Mathematics of Communications, 2010, 4 (1) : 83-99. doi: 10.3934/amc.2010.4.83 |
[17] |
Jamshid Moori, Amin Saeidi. Some designs and codes invariant under the Tits group. Advances in Mathematics of Communications, 2017, 11 (1) : 77-82. doi: 10.3934/amc.2017003 |
[18] |
Yakov Varshavsky. A proof of a generalization of Deligne's conjecture. Electronic Research Announcements, 2005, 11: 78-88. |
[19] |
Karan Khathuria, Joachim Rosenthal, Violetta Weger. Encryption scheme based on expanded Reed-Solomon codes. Advances in Mathematics of Communications, 2021, 15 (2) : 207-218. doi: 10.3934/amc.2020053 |
[20] |
José Moreira, Marcel Fernández, Miguel Soriano. On the relationship between the traceability properties of Reed-Solomon codes. Advances in Mathematics of Communications, 2012, 6 (4) : 467-478. doi: 10.3934/amc.2012.6.467 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]