AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES

Title & Authors
AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES
Kim, Jon-Lark; Lee, Yoonjin;

Abstract
Self-dual codes have been actively studied because of their connections with other mathematical areas including t-designs, invariant theory, group theory, lattices, and modular forms. We presented the building-up construction for self-dual codes over GF(q) with $\small{q{\equiv}1}$ (mod 4), and over other certain rings (see [19], [20]). Since then, the existence of the building-up construction for the open case over GF(q) with $q Keywords building-up construction;linear codes;self-dual codes; Language English Cited by 1. Complementary information set codes over GF(p), Designs, Codes and Cryptography, 2016, 81, 3, 541 2. t-CIS codes over GF(p) and orthogonal arrays, Discrete Applied Mathematics, 2017, 217, 601 3. On the Problem of the Existence of a Square Matrix U Such That UUT=-I over Zpm, Information, 2017, 8, 3, 80 References 1. C. Aguilar Melchor and P. Gaborit, On the classification of extremal [36, 18, 8] binary self-dual codes, IEEE Trans. Inform. Theory, 54 (2008), no. 10, 4743-4750. 2. C. Aguilar-Melchor, P. Gaborit, J.-L. Kim, L. Sok, and P. Sole, Classification of extremal and s-extremal binary self-dual codes of length 38, IEEE Trans. Inform. Theory 58 (2012), no. 4, 2253-2262. 3. R. Alfaro and K. Dhul-Qarnayn, Constructing self-dual codes over$F_q[u]/(u^t)$, Des. Codes Cryptogr. 74 (2015), no. 2, 453-465. 4. R. A. Brualdi and V. Pless, Weight enumerators of self-dual codes, IEEE Trans. Inform. Theory 37 (1991), no. 4, 1222-1225. 5. J. Cannon and C. Playoust, An Introduction to Magma, University of Sydney, Sydney, Australia, 1994. 6. S. T. Dougherty, Shadow codes and weight enumerators, IEEE Trans. Inform. Theory 41 (1995), no. 3, 762-768. 7. T. A. Gulliver and M. Harada, New optimal self-dual codes over GF(7), Graphs Combin. 15 (1999), no. 2, 175-186. 8. T. A. Gulliver, M. Harada, and H. Miyabayashi, Double circulant and quasi-twisted self-dual codes over$\mathbb{F}_5$and$\mathbb{F}_7$, Adv. Math. Commun. 1 (2007), no. 2, 223-238. 9. T. A. Gulliver, J.-L. Kim, and Y. Lee, New MDS or near-MDS self-dual codes, IEEE Trans. Inform. Theory 54 (2008), no. 9, 4354-4360. 10. S. Han, A method for constructing self-dual codes over$\mathbb{Z}_{2^m}$, Des. Codes Cryptogr. 75 (2015), no. 2, 253-262. 11. S. Han, H. Lee, and Y. Lee, Constructions of self-dual codes over$\mathbb{F}_2+u{\mathbb{F}}_2$, Bull. Korean Math. Soc. 49 (2012), no. 1, 135-143. 12. M. Harada, The existence of a self-dual [70, 35, 12] code and formally self-dual codes, Finite Fields Appl. 3 (1997), no. 2, 131-139. 13. M. Harada, personal communication on April 25, 2009. 14. M. Harada and P. R. J. Ostergard, Self-dual and maximal self-orthogonal codes over$\mathbb{F}_7$, Discrete Math. 256 (2002), no. 1-2, 471-477. 15. W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl. 11 (2005), no. 3, 451-490. 16. K. F. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, New York-Berlin, 1982. 17. J.-L. Kim, New extremal self-dual codes of lengths 36, 38 and 58, IEEE Trans. Inform. Theory 47 (2001), 386-393. 18. J.-L. Kim, http://maths.sogang.ac.kr/jlkim/preprints.html. 19. J.-L. Kim and Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004), no. 1, 79-95. 20. J.-L. Kim and Y. Lee, Construction of MDS Self-dual codes over Galois rings, Des. Codes Cryptogr. 45 (2007), no. 2, 247-258. 21. J.-L. Kim and Y. Lee, Self-dual codes using the building-up construction, IEEE International Symposium on Information Theory, 2400-2402, June 28 - July 3, Seoul, Korea, 2009. 22. H. Lee and Y. Lee, Construction of self-dual codes over finite rings$\mathbb{Z}_{p^m}\$, J. Combin. Theory Ser. A 115 (2008), no. 3, 407-422.

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