Submitted papers

35. A Generalized Gleason-Pierce-Ward Theorem,
with Xiaoyu Liu
submitted, 7/23/2008

Abstract: The Gleason-Pierce-Ward theorem gives constraints on the divisor

and field size of a linear divisible code over a finite field

whose dimension is half of the code length. The result is a

departure point for the study of self-dual codes. In recent years,

additive codes have been studied intensively because of their use

to additive quantum codes. In this work, we generalize the

Gleason-Pierce-Ward theorem on linear codes over GF(q), q=p^m,

to additive codes over GF(q). The first step of our proof is an

application of a generalized upper bound on the dimension of a

divisible code determined by its weight spectrum. The bound is

proved by Ward on linear codes over GF(q), and is generalized by

Liu to any code as long as the MacWilliams identities are

satisfied. The trace map and an analogous homomorphism x-x^p on

GF(q) are used to complete our proof.

34. Building-up constructions for self-dual codes,
with Yoonjin Lee
submitted, 6/2/2008

Abstract: The building-up construction for self-dual codes was developed

by the authors and H. Lee over finite fields GF(q) when q is a

power of 2 or q = 1 (mod 4), and then over finite rings Z_p^m with

p =1 (mod 4), and over Galois rings GR(p^m, r) with p = 1 (mod 4)

with any r or p = 3 (mod 4) with even r, where m is any positive

integer. In this paper, we complete the building-up construction for self dual

codes over GF(q) with q = 3 (mod 4), and over Z_p^m and Galois

rings GR(p^m, r) with an odd prime p satisfying p =3 (mod 4). We also

present a building-up construction for self-dual codes over finite chain

rings and p-adic rings Zp^∞ with any odd prime p. As examples, we

reconstruct more than 600 extremal self-dual ternary [28, 14, 9] codes,

improving 32 previously known codes. We also construct many 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 among free

self-dual codes over Z_9 of these lengths.

33. The nonexistence of near-extremal formally self-dual codes,
with Sunghyu Han
resubmitted, May 7, 2008 (5/21/07 original submission)

32. Triple circulant codes based on quadratic residues,
with Sunghyu Han
submitted, Mar. 14, 2008

Abstract: One of the most exciting classes of algebraic codes is the class of quadratic residue

(QR) codes over a finite field. A natural construction doubling the lengths of QR codes

seems to be the double circulant constructions based on quadratic residues given by

Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear

codes based on quadratic residues. We construct many new optimal codes or codes

with the highest known parameters using this construction. In particular, we find

the first example of a ternary [58, 20, 20] code, which improves the previously known

highest minimum distance of any ternary [58, 20] codes.

31. Quantum error-correcting codes from algebraic curves,
with Gretchen L. Matthews
submitted, Mar. 4, 2008, survey paper

30. Formally self-dual additive codes over F_4,
with Sunghyu Han
submitted, Feb. 18, 2008

29. Constructions of self-dual codes over chain rings,
with Steven T. Dougherty and Hongweig Liu,
submitted, Nov. 27, 2007

Accepted papers (in press)

28. A prize problem in coding theory,
To appear in the Book for proceedings D1: Groebner, Coding, and Cryptography (submitted, April 10, 2007, accepted 6/2008)

27. New MDS or near-MDS self-dual codes,
with T. Aaron Gulliver and Yoonjin Lee
To appear in IEEE Transactions on Inform Theory (submitted, Jan. 2007, accepted 6/12/2008)

26. MDS codes over finite principal ideal rings,
with Steven T. Dougherty and Hamid Kulosman,
To appear in Designs, Codes, and Cryptography (submitted, Mar. 5, 2007, accepted 4/22/2008)

25 A quick way to Galois and strongly pure rings,
with Steve Seif and Hamid Kulosman,
To appear in Pan-American Mathematical Journal (submitted, Dec. 31, 2007, accepted 4/12/2008)

24. On self-dual codes over F_5,
with Sunghyu Han,
To appear in Designs, Codes, and Cryptography (submitted 11/6/07, accepted 2/5/08)

23. Skew Hadamard designs and their codes,
with Patrick Sole
to appear in Designs, Codes, and Cryptography. presented at WCC 2007, (submitted 5/30/07, accepted 9/28/07)

22. 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)

21. 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 (accepted 8/9/07) Vol. 308, No. 14. pp. 3115-3124.

20. 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.

19. 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.

18. 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.

17. 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

16. 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

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

14. 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

13. 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

12. 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

11.   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

10.  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

9. 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

8. 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.

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

6. 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.

5. 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.

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

Proceeding Papers (referred)

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 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

3. Identifying codes in q-ary hypercubes,
with Seog-Jin Kim,

2. A Combinatorial Construction of Low-Density Parity-Check Codes,
 with Leo Storme, preprint

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


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