Kernels and p-kernels of pr -ary 1-perfect codes

Designs, Codes, and Cryptography

Volumn 37, Issue 2, 2005, Pages 243-261

  Phelps, K T ^a   Rifa J ^b   Villanueva, M ^b  

^a AUBURN UNIVERSITY   (United States)

^b UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

Author keywords

Kernel; Nonlinear codes; Perfect codes; q ary codes; Rank

Indexed keywords

INVARIANCE; NONLINEAR SYSTEMS; SET THEORY; SWITCHING;

KERNEL; NONLINEAR CODES; PERFECT CODES; Q-ARY CODES; RANK;

CODES (SYMBOLS);

EID: 24944501792     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10623-004-3989-x     Document Type: Article

References (21)

1. S. V. Avgustinovich and F. I. Solov'eva, On projections of perfect binary codes, In Proceedings of the 7th Joint Swedish-Russian International Workshop on Information Theory, St. Petersburg, Russia (1995) pp. 25-26.
2. S. V. Avgustinovich and F. I. Solov'eva, On non-systematic perfect binary codes, Problems of Information Transmission, Vol. 32, No. 3 (1996) pp. 258-261.
3. S. V. Avgustinovich, F. I. Solov'eva and O. Heden, On the ranks and kernels problem of perfect codes, Problems of Information Transmission, Vol. 39, No. 4 (2003) pp. 30-34.
4. H. Bauer, B. Ganter and F. Hergert, Algebraic techniques for nonlinear codes, Combinatorica, Vol. 3 (1983) pp. 21-33.
5. I. F. Blake and R. C. Mullin, The Mathematical Theory of Coding, Academic Press, New York (1975).
6. G. Cohen, I. Honkala, S. Litsyn and A. Lobstein, Covering Codes, North-Holland, Amsterdam (1997).
7. T. Etzion and A. Vardy, Perfect binary codes: constructions, properties, and enumeration, IEEE Transactions on Information Theory, Vol. 40 (1994) pp. 754-763.
8. T. Etzion and A. Vardy, On perfect codes and tilings: problems and solutions, SIAM Journal of Discrete Mathematics, Vol. 11, No. 2 (1998) pp. 205-223.
9. T. Etzion, Nonequivalent q-ary perfect codes, SIAM Journal of Discrete Mathematics, Vol. 9, No. 3 (1996) pp. 413-423.
10. F. I. MacWilliams and N. J. Sloane, The Theory of Error-Correcting Codes, North-Holland, New York (1977).
11. M. LeVan, Designs and Codes, Ph.D. Thesis, Auburn Univesity (1995).
12. B. Lindström, On group and nongroup perfect codes in q symbols, Mathematical Scandinavian, Vol. 25 (1969) pp. 149-158.
13. K. T. Phelps and M. LeVan, Kernels of nonlinear Hamming codes, Designs, Codes and Cryptography, Vol. 6 (1995) pp. 247-257.
14. K. T. Phelps and M. LeVan, Switching equivalence classes of perfect codes, Designs, Codes and Cryptography, Vol. 16 (1999) pp. 179-184.
15. K. T. Phelps and M. Villanueva, Ranks of q-ary 1-perfect codes, Designs, Codes and Cryptography, Vol. 27 (2002) pp. 139-144.
16. K. T. Phelps and M. Villanueva, On perfect codes: rank and kernel, Designs, Codes and Cryptography, Vol. 27 (2002) pp. 183-194.
17. K. T. Phelps, J. Rifà and M. Villanueva, The switching construction and kernels of q-ary 1-perfect codes, In Proceedings of the ACCT-VIII, September 9-14, St. Petersburg, Russia (2002) pp. 222-225.
18. K. T. Phelps, J. Rifà and M. Villanueva, Kernels of q-ary 1-perfect codes, In Proceedings of the Workshop on Coding and Cryptography (WCC), March 24-28, Versailles, France (2003) pp. 375-382.
19. G. S. Shapiro and D. L. Slotnik, On the mathematical theory of error correcting codes, IBM Journal of Research and Development, Vol. 3, No. 1 (1959) pp. 25-34.
20. J. Schönheim, On linear and nonlinear single-error-correcting q-ary perfect codes, Information and Control, Vol. 12 (1968) pp. 23-26.
21. J. L. Vasil'ev, On nongroup close-packed codes, Problemy Kibernetiki, Vol. 8 (1963) pp. 337-339.