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Decoding of $2$D convolutional codes over an erasure channel
Algorithms for the minimum weight of linear codes
1. | Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada, Canada |
References:
[1] |
A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert and A. Wassermann, Error-Correcting Linear Codes, Springer-Verlag, 2006. |
[2] |
A. Betten, H. Fripertinger, A. Kerber, A. Wassermann and K.-H. Zimmermann, Codierungstheorie-Konstruktion und Anwendung linearer Codes, Springer-Verlag, 1998. |
[3] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[4] |
A. Canteaut, V. Lallemand and M. Naya-Plasencia, Related-key attack on full-round PICARO, in Proc. 22nd Int. Conf. Sel. Areas Crypt. 2015 (eds. O. Dunkelman and L. Keliher), Springer, 2015. |
[5] |
W. H. Cunningham, Improved bounds for matroid partition and intersection algorithms, SIAM J. Comput., 15 (1986), 948-957.
doi: 10.1137/0215066. |
[6] |
J. Edmonds, Matroid partition, Math. Decis. Sci., 11 (1968), 335-345. |
[7] |
M. Grassl, Searching for linear codes with large minimum distance, in Discovering Mathematics with Magma - Reducing the Abstract to the Concrete (eds. W. Bosma and J. Cannon), Springer, 2006, 287-313.
doi: 10.1007/978-3-540-37634-7_13. |
[8] |
M. Kiermaier and A. Wassermann, Minimum weights and weight enumerators of $\mathbb Z_4$-linear quadratic residue codes, IEEE Trans. Inf. Theory, 58 (2012), 4870-4883.
doi: 10.1109/TIT.2012.2191389. |
[9] |
E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, 1976. |
[10] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1977. |
[11] |
J. Oxley, Matroid Theory, 2nd edition, Oxford University Press, 2011.
doi: 10.1093/acprof:oso/9780198566946.001.0001. |
[12] |
A. Vardy, The intractability of computing the minimum distance of a code, IEEE Trans. Inf. Theory, 43 (1997), 1757-1766.
doi: 10.1109/18.641542. |
show all references
References:
[1] |
A. Betten, M. Braun, H. Fripertinger, A. Kerber, A. Kohnert and A. Wassermann, Error-Correcting Linear Codes, Springer-Verlag, 2006. |
[2] |
A. Betten, H. Fripertinger, A. Kerber, A. Wassermann and K.-H. Zimmermann, Codierungstheorie-Konstruktion und Anwendung linearer Codes, Springer-Verlag, 1998. |
[3] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[4] |
A. Canteaut, V. Lallemand and M. Naya-Plasencia, Related-key attack on full-round PICARO, in Proc. 22nd Int. Conf. Sel. Areas Crypt. 2015 (eds. O. Dunkelman and L. Keliher), Springer, 2015. |
[5] |
W. H. Cunningham, Improved bounds for matroid partition and intersection algorithms, SIAM J. Comput., 15 (1986), 948-957.
doi: 10.1137/0215066. |
[6] |
J. Edmonds, Matroid partition, Math. Decis. Sci., 11 (1968), 335-345. |
[7] |
M. Grassl, Searching for linear codes with large minimum distance, in Discovering Mathematics with Magma - Reducing the Abstract to the Concrete (eds. W. Bosma and J. Cannon), Springer, 2006, 287-313.
doi: 10.1007/978-3-540-37634-7_13. |
[8] |
M. Kiermaier and A. Wassermann, Minimum weights and weight enumerators of $\mathbb Z_4$-linear quadratic residue codes, IEEE Trans. Inf. Theory, 58 (2012), 4870-4883.
doi: 10.1109/TIT.2012.2191389. |
[9] |
E. L. Lawler, Combinatorial Optimization: Networks and Matroids, Holt, Rinehart and Winston, 1976. |
[10] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1977. |
[11] |
J. Oxley, Matroid Theory, 2nd edition, Oxford University Press, 2011.
doi: 10.1093/acprof:oso/9780198566946.001.0001. |
[12] |
A. Vardy, The intractability of computing the minimum distance of a code, IEEE Trans. Inf. Theory, 43 (1997), 1757-1766.
doi: 10.1109/18.641542. |
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