Combinatorics; Coding Theory; Design Theory
Current research interests focus on coding theory and other combinatorial structures such as designs, and hypergraphs and their properties and as well as related areas of application. Of particular interest are algorithmic and computational methods for enumerating, constructing and studying properties related to these structures. Recently, I have had a supporting role in teaching and occasional research in statistics.
Patric R.J. Ostergaard, O. Pottenen, K. Phelps, The Perfect Binary 1-error correcting codes of length 15: Part II properties, IEEE trans. Inform. Theory, 56(2010) , no 6, 2571-2582
C. Fernandez-Cordoba, K. T. Phelps, On the minimum distance graph of the extended Preparata code, Designs, Codes, and Crypto.57(2010), no.2, 161-170.
P. Zeng, Y. Zhu, K. T. Phelps, Bounds on the Maximum Number of Factors In Designs with two distinct groups of factors,Communications in Statistics - Theory and Methods, 39(2010): 12, 2302 - 2310
ZRM Codes, IEEE Trans. on Information Theory, 54(2008), no. 1, 380-386 (with C. Fernandez, J. Borges)
Intersection of Hadamard Codes,IEEE Trans. on Information Theory,53(2007), no. 5, 1924-1928 (with M. Villanueva)
On the Additive (Z_4-Linear and non-Z_4-Linear) Hadamard Codes. Rank and Kernel. IEEE Trans. on Information Theory,52(2006), no. 1, 316-319 (with J. Rifa, M. Villanueva)
Hadamard codes of length $2^ts$ (s odd). Rank and Kernel,(in Applied algebra, Algebraic algorithms and Error Correcting codes:16th International Symposium, Las Vegas , NV Feb 20-24,2006, eds M. Fossorier, H. Imai, S. Lin, A. Poli) Lecture Notes in Computer Science vol. 3857 (2006) pp328-337 (with J. Rifa, M. Villanueva)
Kernels and $p$-Kernels of $p^r$-ary 1-perfect codes, Designs, Codes and Cryptography, 37(2005) no. 2 pp243-261(with J. Rifa, M. Villanueava)
Quaternary Reed-Muller Codes, IEEE Trans. Information Theory, 51(2005) no. 7 pp2686-2691(with C. Fernandez, J. Borges)
Rank and Kernel of binary Hadamard codes,IEEE Trans. on Information Theory, 51(2005), no.11, 3931-3937 (with J. Rifa, M. Villanueava)
The rank and kernel of 1-perfect additive codes ,IEEE Trans. Information Theory 49(2003), no. 8, 2028-2034 (with J. Borges, J.Rifa).
On $Z_4$ Preparata-like and Kerdock-like codes, IEEE Trans. Information Theory 49(2003), no. 11, 2834-2843(with J. Borges, J. Rifa, V.A.Zinoviev).
Orthogonal quadruple systems and 3-frames, J. Combinatorial Theory, Series A, 104(2003), 115-124 (with W. Muse).
On Perfect Codes: Rank and Kernel, Designs, Codes and Cryptography, 27(2002), no .3, 183-194(with M. Villanueva).
Ranks of q-ary 1-perfect codes, Designs, Codes and Cryptography, 27(2002), 139-144(with M.Villanueva).
On Binary 1-perfect additive codes: Some structural properties, IEEE Trans. Information Theory 48(2002), no. 9, 2587-2591 (with J.Rifa`).
An enumeration of 1-perfect binary codes of length 15, Australasian Journal of Combinatorics, 21(2000) 287-298.