Minimal linear codes arising from blocking sets

Springer Science and Business Media LLC - Tập 53 Số 2 - Trang 327-341 - 2021
Matteo Bonini1, Martino Borello2
1Department of Mathematics, University of Trento, Trento, Italy
2LAGA, UMR 7539, CNRS, Université Paris 13 - Sorbonne Paris Cité, Université Paris 8, 2 Rue de la Liberté, 93526, Saint-Denis, France

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Tài liệu tham khảo

Ashikhmin, A., Barg, A.: Minimal vectors in linear codes. IEEE Trans. Inform. Theory 44(5), 2010–2017 (1998)

Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.A.: On the inherent intractability of certain coding problems. IEEE Trans. Inform. Theory 24(3), 384–386 (1978)

Bartoli, D., Bonini, M.: Minimal linear codes in odd characteristic. IEEE Trans. Inform. Theory 65(7), 4152–4155 (2019)

Bruck, J., Naor, M.: The hardness of decoding linear codes with preprocessing. IEEE Trans. Inform. Theory 36(2), 381–385 (1990)

Chabanne, H., Cohen, G., Patey, A.: Towards secure two-party computation from the wiretap channel. In: Information Security and Cryptology—ICISC 2013, pp. 34–46. Springer, Berlin (2013)

Chang, S., Hyun, J.Y.: Linear codes from simplicial complexes. Des. Codes Cryptogr. 86(10), 2167–2181 (2017)

Clark, P.L.: The Chevalley–Warning theorem (featuring the Erdos–Ginzburg–Ziv theorem). http://math.uga.edu/~pete/4400ChevalleyWarning.pdf

Ding, K., Ding, C.: A class of two-weight and three-weight codes and their applications in secret sharing. IEEE Trans. Inform. Theory 61(11), 5835–5842 (2015)

Ding, C., Heng, Z., Zhou, Z.: Minimal binary linear codes. IEEE Trans. Inform. Theory 64(10), 6536–6545 (2018)

Ding, C., Yuan, J.: Covering and secret sharing with linear codes. In: Calude, C.S., et al. (eds.) Discrete Mathematics and Theoretical Computer Science. Lecture Notes in Computer Science, vol. 2731, pp. 11–25. Springer, Berlin (2003)

Heng, Z., Ding, C., Zhou, Z.: Minimal linear codes over finite fields. Finite Fields Appl. 54, 176–196 (2018)

Huffman, W.C., Pless, V.: Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge (2010)

Hirschfeld, J.W.P.: Projective Geometries Over Finite Fields. Oxford University Press, Oxford (1980)

Massey, J.L.: Minimal codewords and secret sharing. In: Proceedings of the 6th Joint Swedish-Russian International Workshop on Information Theory, pp. 276–279, Mölle (1993)

Massey, J.L.: Some applications of coding theory in cryptography. In: Codes and Cyphers: Cryptography and Coding IV, pp. 33–47, Formara Ltd, Essex (1995)

Mesnager, S., Özbudak, F., Sınak, A.: Linear codes from weakly regular plateaued functions and their secret sharing schemes. Des. Codes Cryptogr. 87(2–3), 463–480 (2019)

Storme, L., De Beule, J. (eds.): Current Research Topics in Galois Geometry. Nova Publishers, New York (2011)

Zhang, W., Yan, H., Wei, H.: Four families of minimal binary linear codes with $$w_ {{\rm min}}/w_ {{\rm max}}\le 1/2$$. Appl. Algebra Engrg. Comm. Comput. 30(2), 175–184 (2019)