Intersections of q-ary perfect codes

Siberian Mathematical Journal

Volumn 49, Issue 2, 2008, Pages 375-382

  Solov'eva, F I ^a   Los, A V ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Hamming code; Intersection of codes; Q ary perfect codes; Switching of components

Indexed keywords

EID: 43349097902     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11202-008-0036-6     Document Type: Article

References (15)

1. Etzion T. and Vardy A., "Perfect binary codes and tilings: problems and solutions," SIAM J. Discrete Math., 11, No. 2, 205-223 (1998).
2. Bar-Yahalom S. E. and Etzion T., "Intersection of isomorphic linear codes," J. Combin. Theory Ser. A, 80, No. 1, 247-256 (1997).
3. Avgustinovich S. V., Heden O., and Solov'eva F. I., "On intersections of perfect binary codes," Bayreuth. Math. Schr., No. 74, 1-6 (2005).
4. Avgustinovich S. V., Heden O., and Solov'eva F. I., "On intersection problem for perfect binary codes," Des. Codes Cryptogr., 39, No. 3, 317-322 (2006).
5. Phelps K. T. and Villanueva M., "Intersection of Hadamard codes," IEEE Trans. Inform. Theory, 53, No. 5, 1924-1928 (2008).
6. Rifá J., Solov'eva F. I., and Villanueva M., "On the intersection of additive perfect codes," IEEE Trans. Inform. Theory, 54, No. 3, 1346-1356 (2008).
7. Rifá J., Solov'eva F. I., and Villanueva M., "On the intersection of additive extended and non-extended perfect codes," Proc. Intern. Workshop on Coding and Cryptography, Versailles, France, April 16-20, pp. 333-341 (2007).
8. Zinov'ev V. A. and Leont'ev V. K., A Theorem on Nonexistence of Perfect Codes over Galois Fields [Preprint] [in Russian], Inst. Probl. Peredachi Inform., Moscow (1972).
9. Zinov'ev V. A. and Leont'ev V. K., "Nonexistence of perfect codes over Galois fields," Problems Control Inform. Theory, No. 2, 123-132 (1973).
10. Tietäväinen A., "On the nonexistence of perfect codes over finite fields," SIAM J. Appl. Math., 24, 88-96 (1973).
11. MacWilliams F. J. and Sloane N. J. A., The Theory of Error-Correcting Codes, North-Holland, Amsterdam (1977).
12. Schönheim J., "On linear and nonlinear single-error-correcting q-nary perfect codes," Inform. Control., 12, No. 1, 23-26 (1968).
13. Phelps K. T. and Villanueva M., "Ranks of q-ary 1 perfect codes," Des. Codes Cryptogr., 27, No. 1-2, 139-144 (2002).
14. Los A. V., "Construction of perfect q-ary codes by switchings of simple components," Problems Inform. Transmission, 42, No. 1, 30-37 (2006).
15. Solov'eva F. I. and Los' A. V., "On intersections of q-ary perfect codes," Proc. Tenth Int. Workshop "Algebraic and Combinatorial Coding Theory," Zvenigorod, Russia, September 3-9, 2006, pp. 244-247.