New Hermitian self-dual MDS or near-MDS codes over finite fields

Authors

  • Djoko Suprijanto Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung

DOI:

https://doi.org/10.5614/j.math.fund.sci.2014.46.1.6

Keywords:

decoding error probability performance, Hermitian self-dual codes, lexicographical ordering, MDS codes, near-MDS codes.

Abstract

A linear code over a finite field is called Hermitian self-dual if the code is self-dual under the Hermitian inner-product. The Hermitian self-dual code is called MDS or near-MDS if the code attains or almost attains the Singleton bound. In this paper we construct new Hermitian self-dual MDS or near-MDS codes over and of length up to 14.

References

MacWilliams, F.J. & Sloane, N.J.A., TheTheory of Error-Correcting Codes, Elsevier, Amsterdam, 1977.

de Boer, M.A., Almost MDS codes, Designs, Codes, and Cryptography,9(2), pp.143-155, 1996.

Dodunekov, S. & Landjev, I.N., On Near-MDS codes, J. Geom.,54(1-2), pp.30-43, 1995.

Dodunekov, S., Applications of Near-MDS Codes in Cryptography, in Enhancing Cryptographic Primitive with Techniques from Error-Correcting Codes, Preneel, B., et al. (eds), IOS Press, Amsterdam, pp. 81-86, 2009.

Zhou, Y., Wang, F., Xin, Y., Luo, S., Qing, S. & Yang, Y., A Secret Sharing Schemes Based on Near-MDS Codes, Proceedings of IC-NIDC 2009, pp. 833-836, 2009.

Georgiou, S. & Koukouvinos, C., MDS Self-Dual Codes Over Large Prime Fields, Finite Field Appl.,8(4), pp. 455-470, 2002.

Betsumiya, K., Georgiou, S., Gulliver, T.A., Harada, M. & Koukouvinos, C., On Self-Dual Codes Over Some Prime Fields,Discrete Math.,262(1-3), pp. 37-58, 2003.

Kim, J.-L. & Lee, Y., Euclidean and Hermitian Self-Dual MDS Codes Over Larger Finite Fields, J. Combin. Theory Ser. A,105(1), pp. 79-95, 2004.

Harada, M. & Kharaghani, H., Orthogonal Designs and MDS Self-dual Codes, Austral. J. Combin.,35, pp. 57-67, 2006.

Gulliver, T.A., Kim, J.-L. & Lee, Y., New MDS or Near-MDS Self-Dual Codes, IEEE Inform. Theory,54(9), pp. 4354-4360, 2008.

Elviyenty, M. & Suprijanto, D., An Algorithm to Construct New (near-) MDS or (near-)MDR Self-Dual Codes over Finite Rings in The 5thInternational Conference On Research And Education In Mathematics (ICREM 5)AIP Conf. Proc.,1450, pp.205-210, 2012.

Bosma, W. & Canon. J, Handbook of Magma Functions, Sydney, Australia, 2006. (preprint).

Faldum, A., Lafuente, J., Ochoa, G. &Willems, W., Error Probabilities for Bounded Distance Decoding, Designs, Codes, and Crypt.,40(2), pp. 237-252, 2006.

Bouyuklieva, S., Malevich, A. &Willems, W., On the Performance of Binary Extremal Self-Dual Codes, Adv. Math. Commun.,5(2), pp. 267-274, 2011.

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Published

2014-04-01

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