Submitted papers

Stefka Bouyuklieva, Nikolay Yankov and Jon-Lark Kim, submitted on Jan. 19, 2012

Claude Carlet, Philippe Gaborit, Jon-Lark Kim, and Patrick Sole, submitted on Oct. 6, 2011

42. Computational results of duadic double circulant codes

Sunghyu Han and Jon-Lark Kim, submitted on Oct. 17, 2010

Abstract: Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. We describe a method to construct duadic double circulant codes using 4-cyclotomic cosets and give such duadic double circulant codes of proper lengths over F_2, F_3, F_4, F_5, and F_7. In particular, we find a new ternary self-dual [76,38,18] code and rediscover easily optimal binary self-dual codes with parameters [66,33,12], [68,34,12], [86,43,16], and [88,44,16] as well as a formally self-dual binary [82,41,14] code.

41. An efficient construction of self-dual codes,
Yoonjin Lee and Jon-Lark Kim
revised and resubmitted 1/26/2012

(File for new self-dual [32,16,9] codes over GF(3) with trivial automorphsim groups) (note: Title change from Building-up constructions for self-dual codes)

Abstract: We complete the building-up construction for self-dual codes by resolving the open cases over GF(q) with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings GR(p^m,r) with an odd prime p satisfying $p \equiv 3 \pmod 4$ with r odd. We also extend the building-up construction for self-dual codes to finite chain rings. Our building-up construction produces many new interesting self-dual codes. In particular, we construct 945 new extremal self-dual ternary [32,16,9] codes, each of which has a trivial automorphism group. We also obtain many new self-dual codes over Z_9 of lengths 12, 16, 20 all with minimum Hamming weight 6, which is the best possible minimum Hamming weight that free self-dual codes over Z_9 of these lengths can attain. From the constructed codes over Z_9, we reconstruct optimal Type I lattices of dimensions 12, 16, 20, and 24 using Construction A; this shows that our building-up construction can make a good contribution for finding optimal Type I lattices as well as self-dual codes.We also find new optimal self-dual [16,8,7] codes over GF(7) and new self-dual codes over GF(7) with the best known parameters [24,12,9].

Accepted papers (in press)

Sunghyu Han, Jon-Lark Kim, Heisook Lee, and Yoonjin Lee, to appear in Finite Fields and Their Applications (submitted on Oct. 12, 2011, accepted on 12/28/2012)

Carlos Aguilar-Melchor, Philippe Gaborit, Jon-Lark Kim, Lin Sok, and Patrick Sole, submitted on Apr. 4, 2011, to appear IEEE Trans. Information Theory.

Jon-Lark Kim and Seog-Jin Kim, To appear in Discrete Applied Math, (accepted on July 22, 2011)

37. Type I codes over GF(4),
with Hyun Kwang Kim and Dae Kyu Kim
To appear in Ars Combinatoria, (accepted on May 17, 2007)

Printed Journal Papers (contents in journals may be modified)

36. Formally self-dual additive codes over F_4,
with Sunghyu Han,
in the special issue of J. Symbolic Computation on Algebraic Coding Theory and Application, Vol. 45, NO. 7 (2010), 787-799

35. Self-dual codes over Commutative Frobenius rings,
with Steven T. Dougherty, Hamid Kulosman, and Hongwei Liu, Finite Fields and Their Applications, Vol.16, No.1 (2010), 14-26.

34. Constructions of self-dual codes over finite commutative chain rings,
with Steven T. Dougherty and Hongweig Liu, (file for generator matrices ) Int. J. Inform and Coding Theory as a special issue in Honour of the Retirement of Vera Pless, Vol.1 No 2 (2010), 171-190.

33. Identifying codes in q-ary hypercubes,
with Seog-Jin Kim (resubmitted 4/17/2009, accepted 4/22/2009) Bulletin of the Institute of Combinatorics and its Application, Volume 59 (2010), 93-102.

32. A generalized Gleason-Pierce-Ward theorem,
with Xiaoyu Liu
Designs, Codes, and Cryptography (submitted 7/23/2008, resubmitted 12/01/2008, accepted 4/1/09), Vol. 52, No. 3 (2009), pp. 363-380.

31. The nonexistence of near-extremal formally self-dual codes,
with Sunghyu Han
Designs, Codes, and Cryptography (second submission 8/21/08,

Accepted 9/29/2008, (5/21/07 original submission)), Vol. 51 (2009), No.1, pp. 69-77.

30.MDS codes over finite principal ideal rings,
with Steven T. Dougherty and Hamid Kulosman,
Designs, Codes, and Cryptography (submitted, Mar. 5, 2007, accepted 4/22/2008) Vol. 50 (2009), No. 1, pp. 77-92.

29. A quick way to Galois and strongly pure rings,
with Steve Seif and Hamid Kulosman,
Pan-American Mathematical Journal (submitted, Dec. 31, 2007, accepted 4/12/2008) Vol. 18 (2008), No. 4, pp. 39-44.

28. Skew Hadamard designs and their codes,
with Patrick Sole
Designs, Codes, and Cryptography. presented at WCC 2007, (submitted 5/30/07, accepted 9/28/07), Special issue: Coding and Cryptography. In Memory of Hans Dobbertin, WCC 2007, Vol. 49 (2008), pp. 135-145.

27. New MDS or near-MDS self-dual codes,
with T. Aaron Gulliver and Yoonjin Lee
IEEE Transactions on Inform Theory (submitted, Jan. 2007, accepted 6/12/2008), Vol. 54 (2008), No. 9, pp. 4354-4360.

26. On self-dual codes over F_5,
with Sunghyu Han,
Designs, Codes, and Cryptography (submitted 11/6/07, accepted 2/5/08), Vol. 48 (2008) No. 1., pp. 43-58.

25. Nonbinary Quantum Error-Correcting Codes from Algebraic Curves,
with Judy L. Walker,
Discrete Math as a special issue of Com2MaC conference, July 2004, Pusan, Korea, Vol. 308, No. 14 (2008) pp. 3115-3124.

24. Upper bounds for the lengths of s-extremal codes over F_2, F_4, and F_2+uF_2,
with Sunghyu Han
IEEE Trans. Inform.Theory, (submitted 3/5/07, accepted 9/25/07), Vol. 54 (2008), No. 1, pp. 418-422.

23. Construction of MDS self-dual codes over Galois rings,
with Yoonjin Lee
Designs, Codes, and Cryptography (submitted 5/21/07, accepted 7/20/07), Vol. 45 (2007), No. 2, pp. 247-258.

22. A Note on Formally Self-Dual Even Codes of Length Divisible by 8
with Vera Pless,
Finite Fields and Their Applications, Vol. 13, No. 2, (2007), pp. 224-229.

21. Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles,
with Keith E. Mellinger and Leo Storme
Designs, Codes and Cryptography, 42 (2007), 73-92.

20. Double circulant codes from two class association schemes with Steven T. Dougherty and Patrick Sole
Advances in Mathematics of Communications, 1 (2007), 45-64.

with E. P. Bautista, Philippe Gaborit, and Judy Walker
Advances in Mathematics of Communications (full version of ISIT 2006 version), 1 (2007), 111-130

18. Explicit construction of families of LDPC codes with no 4-cycles, (ps)
with U.N. Peled, I. Perepelitsa, V. Pless and S. Friedland,
IEEE Trans. Inform. Theory, Vol. 50 (Oct 2004), pp. 2378-2388.

17. Circulant based extremal additive self-dual codes over GF(4), (ps)
with T. Aaron Gulliver,
IEEE Trans. on Inform. Theory, Vol. 40 (Feb. 2004), pp. 359-366 .

16.   Euclidean and Hermitian self-dual MDS codes over large finite fields, (ps)
with Yoonjin Lee,
J. Combinatorial Theory, Ser. A, 105 (2004) pp. 79-95.

15Designs in Additive Codes over GF(4) (revised version of 38th Allerton conference)
with Vera Pless,
Designs, Codes and Cryptography, Vol 30, (2003), pp. 187-199.

14. Projections of binary linear codes onto larger fields,(pdf) (revised as of June 12, 2003)
with K. Mellinger and V. Pless,
SIAM journal on Discrete Math, Vol 16, No. 4, (2003), pp. 591-603

13. Decoding Binary R(2,5) by Hand(ps), (revised June 22, 2001)
with Philippe Gaborit and Vera Pless,
Discrete Math. Vol. 264 (2003), pp. 55-73.

12. Construction of Some Extremal Self-Dual Codes,
with T. Aaron Gulliver and Masaaki Harada,
Discrete Math, Vol. 263 (2003), pp. 81-91.

11. New Self-Dual Codes over GF(4) with the Highest Known Minimum Weights, (full version)
IEEE Trans. Inform. Theory,  Vol. 47 (May 2001), pp. 1575-1580.

10. New extremal self-dual codes of lengths 36,38, and 58(ps), revised,
IEEE Trans. on Inform. Theory, Vol. 47 (Jan. 2001), pp. 386-393.

9. Relation Between Weight Distribution and Combinatorial Identities(ps),
Bulletin of the Institute of Combinatorics and its Application, Canada, Vol 31, Jan. 2001,
69-79.

Book Chapters

8. A prize problem in coding theory,
the Book for proceedings D1: Groebner, Coding, and Cryptography (submitted, April 10, 2007, accepted 6/2008), Part II, Section 5.

7. Quantum error-correcting codes from algebraic curves,
with Gretchen L. Matthews
submitted, Mar. 4, 2008, survey paper, Advances in algebraic geometry codes, ed. E. Martinez-Moro,

C. Munuera, and D. Ruano, Series on Coding Theory and Cryptology, 5, World Scientific Publishing Co.

Pte. Ltd., Hackensack, NJ, 2008

6. Remarks on s-extremal codes,
Advances in Coding Theory and Cryptology  Series on Coding Theory and Cryptology, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007 (accepted in March 2007) pp. 101-113.

Proceeding Papers (referred)

5. Self-dual codes using the building-up construction, Jon-Lark Kim and Yoonjin Lee, Proc. of 2009 IEEE International Symposium on Information Theory, Seoul, 2009, pp. 2400-2402.

4. Construction of cubic self-dual codes, Sunghyu Han, Jon-Lark Kim, Heisook Lee, and Yoonjin Lee, Proc. of 2009 IEEE International Symposium on Information Theory, Seoul, 2009, pp. 2396-2399.

3. New quantum-error-correcting codes from Hermitian self-orthogonal codes over GF(4) (pdf), (referred)
Proceedings of the sixth international conference on Finite fiedls and applications, at Oaxaca, Mexico, May 21-25, 01. 2001, Springer Verlag (2002), pp. 209-213.

with Philippe Gaborit, W. Cary Huffman, and Vera Pless,
DIMACS Workshop on Codes and Association Schemes, DIMACS Series in Discrete Math. and Theoretical Computer Science, American Mathematical Society, Vol. 56 (2001), pp. 135-149.

1. Decoding Some Doubly-Even Self-Dual [32,16,8] Codes by Hand(ps),(referred)
with  Vera Pless,
Proceedings of XXVth Ohio State-Denison conference on Codes and Designs(May, 2000), Sept. 25, 00. pp. 165-178.

Proceeding Papers (non refereed)

4. Dual cyclic codes with two zeros,
Proceedings of the 40th Allerton Conference on Communication, Control, and Computing (10/2-10/4) at Allerton, IL., Oct. 2002, pp. 1017-1023.

3. Explicit construction of LDPC codes with girth at least six,
with Uri N. Peled , Irina Perepelitsa, and Vera Pless,
Proceedings of the 40th Allerton Conference on Communication, Control, and Computing (10/2-10/4) at Allerton, IL., Oct. 2002, pp. 1024-1031.

2. Designs in Additive Codes over GF(4),
with Vera Pless,
Proceedings of the 38th Allerton Conference on Communication, Control and Computing, UIUC, Oct. 2000, pp. 1010-1018.

1. On the Classification of Extremal Additive  Codes over GF(4)(ps),
with Philippe  Gaborit, W. Cary Huffman, and Vera Pless,
Proceedings of the 37th Allerton Conference on Communication, Control and Computing, UIUC, Sep. 1999, pp. 535-544.

Preprint

1. Codes constructed from Non-Symmetric Association Schemes(ps),
preprint, Dec. 1997,