Submitted papers

50. An efficient construction of self-dual codes,
Yoonjin Lee and Jon-Lark Kim
submitted 4/22/2014

(note: Title change from Building-up constructions for self-dual codes)

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 $q \equiv 1 \pmod 4$, and over other certain rings ({KimLee},{KimLee2}). Since then, the existence of the building-up construction for the open case over $GF(q)$ with $q=p^r \equiv 3 \pmod 4$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with $r$ odd has not been solved. In this paper, we answer it positively by presenting the building-up construction explicitly. As examples, we present new optimal self-dual $[16,8,7]$ codes over $GF(7)$ and new self-dual codes over $GF(7)$ with the best known parameters $[24,12,9]$.

49. Multiply Constant Weight Codes and an Application to the Loop Physically Unclonable Function,
Yeow Meng Chee, Zouha Cherif, Jean-Luc Danger, Sylvain Guilley, Han Mao Kiah, Jon-Lark Kim, Patrick Sole, Xiande Zhang,
submitted 10/24/2013

Abstract: We introduce the class of multiply constant weight codes to improve the reliability of certain physically unclonable function (PUF) response. We extend classical coding methods to construct multiply constant weight codes from known $q$-ary and constant weight codes. Analogues of Johnson bounds are derived and are shown to be asymptotically tight to a constant factor under certain conditions. We also examine the rates of the multiply constant weight codes and interestingly, demonstrate that these rates are the same as those of constant weight codes of suitable parameters. Asymptotic analysis of our code constructions is provided.

48. Powers, Pythagorean triples, and Fermat’s Last Theorem in carryless arithmetic mod 10,
Joon Yop Lee and Jon-Lark Kim,
submitted 4/18/2013

Abstract: We study carryless arithmetic mod 10 introduced by Applegate, LeBrun, and Sloane. We know that this arithmetic corresponds to the algebra in $\mathbb Z_{10}[x]$. In particular, we give an explicit formula for the number of $k$-digit carryless $m$th powers in $\mathbb Z_{10}[x]$ ($m \ge 2$), which was known only for $m=2$. We give a complete characterization of the Pythagorean triples $(f(x), g(x), h(x))$ in $\mathbb Z_{10}[x]$. We also prove the falsity of the Fermat Last Theorem, that is, there are infinitely many solutions to $f(x)^m + g(x)^m = h(x)^m$ for any $m\ge 3$. Furthermore, we give a complete solution to $f(x)^{2^n}+g(x)^{2^n}=h(x)^{2^n}$ for any $n\ge 2$.

47. Higher-order CIS codes,
Claude Carlet, Finley Freibert, Sylvain Guilley, Michael Kiermaier, Jon-Lark Kim, and Patrick Sole,
submitted 12/3/2012, revised submission 3/23/2014

Abstract: We introduce  {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise disjoint information sets. The duals of such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks.As in the case of codes for error correction, given the length and the dimension of a $t$-CIS code, we look for the highest possible minimum distance. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order $3$ is derived by a counting argument. General constructions based on cyclic and quasi-cyclic codes and on the building up construction are given.  A formula similar to a mass formula is given. A classification of 3-CIS codes of length $\le 12$ is given. Nonlinear codes better than linear codes are derived by taking binary images of $\Z_4$-codes. A general algorithm based on Edmonds' basis packing algorithm from matroid theory is developed with the following property: given a binary linear code of rate $1/t$ it either provides $t$ disjoint information sets or proves that the code is not $t$-CIS. Using this algorithm, all optimal or best known $[tk, k]$ codes where $t=3, 4, \dots, 256$ and $1 \le k \le \lfloor 256/t \rfloor$ are shown to be $t$-CIS for all such $k$ and $t$, except for $t=3$ with  $k=44$ and $t=4$ with $k=37$.

Accepted papers (in press)

46. Codes over Rings and Hermitian Lattices
Steven Dougherty, Jon-Lark Kim, and Yoonjin Lee,
to appear in Designs, Codes and Cryptography (accepted on 4/15/2014)

Printed Journal Papers (contents in journals may be modified)

45. Optimal subcodes and optimum distance profiles of self-dual codes,
Finley Freibert and Jon-Lark Kim,

Finite Fields and Their Applications, 24 (2014) 146-164.

44.
Finley Freibert and Jon-Lark Kim,
A special issue of Applicable Algebra in Engineering, Communication and Computing devoted to Coding Theory and Cryptography, 24 (2013) 215-224.

Stefka Bouyuklieva, Nikolay Yankov and Jon-Lark Kim, Finite Fields and Their Applications, 18 (2012) 1104-1113.

Claude Carlet, Philippe Gaborit, Jon-Lark Kim, and Patrick Sole, IEEE Trans. Inform. Theory, 58 (9) (2012), pp. 6000-6011.

41. Computational results of duadic double circulant codes

Sunghyu Han and Jon-Lark Kim, J. Applied Mathematics and Computing, 40 (2012), no. 1-2, 33-43.

Sunghyu Han, Jon-Lark Kim, Heisook Lee, and Yoonjin Lee, Finite Fields and Their Applications,

Finite Fields and Their Applications, 18 (2012), no. 3, 613-633.

Carlos Aguilar-Melchor, Philippe Gaborit, Jon-Lark Kim, Lin Sok, and Patrick Sole, IEEE Trans. Information Theory, 58 (2012), no. 4, 2253-2262.

Jon-Lark Kim and Seog-Jin Kim, Discrete Applied Math.,159 (2012), no. 18, 2222-2228.

37. Type I codes over GF(4),
with Hyun Kwang Kim and Dae Kyu Kim Ars Combinatoria, 106 (2012), 173-191. (cf. accepted on May 17, 2007)

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
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

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  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,