**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.** Optimal subcodes of formally
self-dual codes and their optimum distance profiles,**

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.

43**. Classification
of binary self-dual [48,24,10] codes with an
automorphism of odd prime order **

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

42**. A new class of
codes for Boolean masking of cryptographic computations**

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

(Data:
Classification
of CIS codes of lengths <=12 (word file) )

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.

40**. Construction
of quasi-cyclic self-dual codes**

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.

39**. Classification
of extremal and s-extremal binary
self-dual codes of length 38**

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

38**. The
2-distance coloring of the Cartesian product of cycles using optimal Lee codes**

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

(File for all
formally self-dual (6,2^6,3) additive codes over GF(4))

(File for
formally self-dual (9,2^9,4) additive codes over
GF(4))

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.

19. **s-extremal
additive F_4 codes**

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.*

15. **Designs 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 2*009 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 2*009
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.*

2. **On Additive GF(4)
Codes(ps),**(referred)

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 40 ^{th} 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 40 ^{th} 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,

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