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On extendability of additive code isometries
Yet another variation on minimal linear codes
1. | Télécom ParisTech, UMR 5141, CNRS, 46 rue Barrault, 75634 Paris Cedex 13, France, France |
2. | University of Paris XIII and Paris VIII, Télécom ParisTech, LAGA, UMR 7539, CNRS, Sorbonne Paris Cité, France |
References:
[1] |
N. Alon, G. Cohen, M. Krivilevitch and S. Litsyn, Generalized hashing and applications,, JCT-A, 104 (2003), 207.
doi: 10.1016/j.jcta.2003.08.001. |
[2] |
A. Ashikhmin and A. Barg, Minimal vectors in linear codes,, IEEE Trans. Inf. Theory, 44 (1998), 2010.
doi: 10.1109/18.705584. |
[3] |
A. Ashikhmin, A. Barg, G. Cohen and L. Huguet, Variations on minimal codewords in linear codes,, in Applied Algebra, (1995), 96.
doi: 10.1007/3-540-60114-7_7. |
[4] |
A. Bassa, P. Beelen, A. Garcia and H. Stichtenoth, Towers of function fields over non-prime finite fields,, Moscow Math. J., 15 (2015), 1. Google Scholar |
[5] |
G. Brassard, C. Crépeau and M. Santha, Oblivious transfers and intersecting codes,, IEEE Trans. Inf. Theory, 42 (1996), 1769.
doi: 10.1109/18.556673. |
[6] |
H. Chabanne, G. Cohen and A. Patey, Towards secure two-party computation from the wire-tap channel,, in Information Security and Cryptology-ICISC 2013, (2013), 34.
doi: 10.1007/978-3-319-12160-4_3. |
[7] |
G. Cohen, S. Encheva, S. Litsyn and H.-G. Schaathun, Intersecting codes and separating codes,, Discrete Appl. Math., 128 (2003), 75.
doi: 10.1016/S0166-218X(02)00437-7. |
[8] |
G. Cohen and A. Lempel, Linear intersecting codes,, Discrete Math., 56 (1985), 35.
doi: 10.1016/0012-365X(85)90190-6. |
[9] |
G. Cohen, S. Mesnager and A. Patey, On minimal and quasi-minimal linear codes,, in Proc. 14th Int. Conf. Crypt. Coding, (2013), 85.
doi: 10.1007/978-3-642-45239-0_6. |
[10] |
G. Cohen and H.-G. Schaathun, Upper bounds on separating codes,, IEEE Trans. Inf. Theory, 50 (2004), 1291.
doi: 10.1109/TIT.2004.828140. |
[11] |
C. Ding and J. Yuan, Covering and secret sharing with linear codes,, in DMTCS, (2003), 11.
doi: 10.1007/3-540-45066-1_2. |
[12] |
E. N. Gilbert, A comparison of signaling alphabets,, Bell Syst. Techn. J., 31 (1952), 504. Google Scholar |
[13] |
F. J. MacWilliams and N. J. Sloane, The theory of error-correcting codes,, North Holland, (1977). Google Scholar |
[14] |
J. L. Massey, Minimal codewords and secret sharing,, in Proc. 6th Joint Swedish-Russian Int. Workshop Info. Theory, (1993), 276. Google Scholar |
[15] |
J. L. Massey, Some applications of coding theory in cryptography,, in Codes and Cyphers: Cryptography and Coding IV (ed. P.G. Farrell), (1995), 33. Google Scholar |
[16] |
H. Randriambololona, $(2,1)$-separating systems beyond the probabilistic bound,, Israel J. Math., 195 (2013), 171.
doi: 10.1007/s11856-012-0126-9. |
[17] |
H. Randriambololona, Asymptotically good binary linear codes with asymptotically good self-intersection spans,, IEEE Trans. Inf. Theory, 59 (2013), 3038.
doi: 10.1109/TIT.2013.2237944. |
[18] |
H. Randriambololona, On products and powers of linear codes under componentwise multiplication,, in Proc. 14th Int. Conf. Arithm. Geom. Crypt. Coding Theory (AGCT-14), (2015), 3.
doi: 10.1090/conm/637/12749. |
[19] |
H. G. Schaathun, The Boneh-Shaw fingerprinting scheme is better than we thought,, IEEE Trans. Inf. Forensics Sec., 1 (2006), 248. Google Scholar |
[20] |
Y. Song and Z. Li, Secret sharing with a class of minimal linear codes,, preprint, (). Google Scholar |
[21] |
Y. Song, Z. Li, Y. Li and J. Li, A new multi-use multi-secret sharing scheme based on the duals of minimal linear codes,, Sec. Commun. Netw., 8 (2015), 202. Google Scholar |
[22] |
M. A. Tsfasman and S. G. Vladut, Algebraic Geometric Codes,, Kluwer, (1991).
doi: 10.1007/978-94-011-3810-9. |
show all references
References:
[1] |
N. Alon, G. Cohen, M. Krivilevitch and S. Litsyn, Generalized hashing and applications,, JCT-A, 104 (2003), 207.
doi: 10.1016/j.jcta.2003.08.001. |
[2] |
A. Ashikhmin and A. Barg, Minimal vectors in linear codes,, IEEE Trans. Inf. Theory, 44 (1998), 2010.
doi: 10.1109/18.705584. |
[3] |
A. Ashikhmin, A. Barg, G. Cohen and L. Huguet, Variations on minimal codewords in linear codes,, in Applied Algebra, (1995), 96.
doi: 10.1007/3-540-60114-7_7. |
[4] |
A. Bassa, P. Beelen, A. Garcia and H. Stichtenoth, Towers of function fields over non-prime finite fields,, Moscow Math. J., 15 (2015), 1. Google Scholar |
[5] |
G. Brassard, C. Crépeau and M. Santha, Oblivious transfers and intersecting codes,, IEEE Trans. Inf. Theory, 42 (1996), 1769.
doi: 10.1109/18.556673. |
[6] |
H. Chabanne, G. Cohen and A. Patey, Towards secure two-party computation from the wire-tap channel,, in Information Security and Cryptology-ICISC 2013, (2013), 34.
doi: 10.1007/978-3-319-12160-4_3. |
[7] |
G. Cohen, S. Encheva, S. Litsyn and H.-G. Schaathun, Intersecting codes and separating codes,, Discrete Appl. Math., 128 (2003), 75.
doi: 10.1016/S0166-218X(02)00437-7. |
[8] |
G. Cohen and A. Lempel, Linear intersecting codes,, Discrete Math., 56 (1985), 35.
doi: 10.1016/0012-365X(85)90190-6. |
[9] |
G. Cohen, S. Mesnager and A. Patey, On minimal and quasi-minimal linear codes,, in Proc. 14th Int. Conf. Crypt. Coding, (2013), 85.
doi: 10.1007/978-3-642-45239-0_6. |
[10] |
G. Cohen and H.-G. Schaathun, Upper bounds on separating codes,, IEEE Trans. Inf. Theory, 50 (2004), 1291.
doi: 10.1109/TIT.2004.828140. |
[11] |
C. Ding and J. Yuan, Covering and secret sharing with linear codes,, in DMTCS, (2003), 11.
doi: 10.1007/3-540-45066-1_2. |
[12] |
E. N. Gilbert, A comparison of signaling alphabets,, Bell Syst. Techn. J., 31 (1952), 504. Google Scholar |
[13] |
F. J. MacWilliams and N. J. Sloane, The theory of error-correcting codes,, North Holland, (1977). Google Scholar |
[14] |
J. L. Massey, Minimal codewords and secret sharing,, in Proc. 6th Joint Swedish-Russian Int. Workshop Info. Theory, (1993), 276. Google Scholar |
[15] |
J. L. Massey, Some applications of coding theory in cryptography,, in Codes and Cyphers: Cryptography and Coding IV (ed. P.G. Farrell), (1995), 33. Google Scholar |
[16] |
H. Randriambololona, $(2,1)$-separating systems beyond the probabilistic bound,, Israel J. Math., 195 (2013), 171.
doi: 10.1007/s11856-012-0126-9. |
[17] |
H. Randriambololona, Asymptotically good binary linear codes with asymptotically good self-intersection spans,, IEEE Trans. Inf. Theory, 59 (2013), 3038.
doi: 10.1109/TIT.2013.2237944. |
[18] |
H. Randriambololona, On products and powers of linear codes under componentwise multiplication,, in Proc. 14th Int. Conf. Arithm. Geom. Crypt. Coding Theory (AGCT-14), (2015), 3.
doi: 10.1090/conm/637/12749. |
[19] |
H. G. Schaathun, The Boneh-Shaw fingerprinting scheme is better than we thought,, IEEE Trans. Inf. Forensics Sec., 1 (2006), 248. Google Scholar |
[20] |
Y. Song and Z. Li, Secret sharing with a class of minimal linear codes,, preprint, (). Google Scholar |
[21] |
Y. Song, Z. Li, Y. Li and J. Li, A new multi-use multi-secret sharing scheme based on the duals of minimal linear codes,, Sec. Commun. Netw., 8 (2015), 202. Google Scholar |
[22] |
M. A. Tsfasman and S. G. Vladut, Algebraic Geometric Codes,, Kluwer, (1991).
doi: 10.1007/978-94-011-3810-9. |
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