publication . Preprint . 2016

Construction of MDS self-dual codes from orthogonal matrices

Shi, Minjia; Sok, Lin; Solé, Patrick;
Open Access English
  • Published: 25 Oct 2016
Abstract
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS self-dual codes over both small and large prime fields are constructed.
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free text keywords: Computer Science - Information Theory
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21 references, page 1 of 2

[1] C. Aguilar-Melchor and P. Gaborit, “On the classification of extremal [36, 18, 8] binary self-dual codes,” IEEE Transactions on Information Theory, vol. 54, no 10, pp. 4743-4750, 2008.

[2] C. Aguilar-Melchor, P. Gaborit, J-L. Kim, L. Sok, P. Sol´e, “Classification of extremal and s-extremal binary self-dual codes of length 38,” IEEE Trans. on Information Theory IT-58 (2012) 2253-2252.

[3] K. Betsumiya, S. Georgiou, T. A. Gulliver, M. Harada and C. Koukouvinos, “On self-dual codes over some prime fields,” Discrete Mathematics 262 (2003) 37-58. [OpenAIRE]

[4] W. Bosma and J. Cannon, Handbook of Magma Functions, Sydney, 1995.

[5] J.M. Chao and H. Kaneta, “Classical arcs in P G(r, q) for 11 ≤ q ≤ 19,” Discrete Math. 174 (1997) 87-94. [OpenAIRE]

[6] J.H. Conway and N.J.A. Sloane, “A new upper bound on the minimal distance of self-dual codes,” IEEE Trans. Inf. Th., vol. 36, pp. 1319- 1333, 1990.

[7] P. Gaborit and A. Otmani, “Experimental constructions of self-dual codes,” Finite Fields and their Applications, vol. 9, no. 3, pp. 372-394, July 2003. [OpenAIRE]

[8] S. Georgiou and C. Koukouvinos, “MDS Self-Dual Codes over Large Prime Fields,” Finite Fields and Their Applications vol. 8, pp. 455-470, 2002. [OpenAIRE]

[9] M. Grassl and T. A. Gulliver, “On Self-Dual MDS Codes” ISIT 2008, Toronto, Canada, July 6 -11, 2008

[10] K. Guenda, “New MDS self-dual codes over finite fields,” Des. Codes Cryptogr. (2012) 62:31-42.

[11] W.C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.

[12] L. E. Dickson, History of the Theory of Numbers, Vol. 2. Chelsea Publishing Co., New York 1920.

[13] L. F. Jin and C. P. Xing, New MDS self-dual codes from generalized Reed-Solomon codes, arXiv:1601.04467v1, 2016.

[14] J-L. Kim and Y. Lee, “Construction of MDS self-dual codes over Galois rings,” Des. Codes Cryptogr. (2007) 45:247-258.

[15] F.J. MacWilliams, N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam 1977.

21 references, page 1 of 2
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