Cocyclic Hadamard codes

IEEE Transactions on Information Theory

Volumn 46, Issue 4, 2000, Pages 1545-1550

  Horadam, Kathy J ^a,b   Udaya, Parampalli ^a,b  

^a IEEE   (United States)

^b RMIT UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMAL MAPPING; FOURIER TRANSFORMS; MATRIX ALGEBRA; POLYNOMIALS; THEOREM PROVING; VECTORS;

COCYCLIC HADAMARD CODE; GENERALIZED PLOTKIN BOUND; HADAMARD MATRIX; PRESEMIFIELD MULTIPLICATION COCYCLE; QUATERNARY CODE; RELATIVE DIFFERENCE SET;

BINARY CODES;

EID: 0034226243     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.850692     Document Type: Article

References (23)

1. J. P. Arpasi and R. Palazzo Jr., An algorithm to construct strongly controllable group codes from an abstract group, in Proc. 1998 IEEE Int. Symp. Information Theory, Cambridge, MA, Aug. 1998, p. 154.
2. E. F. Assmus Jr. and J. D. Key, Designs and Their Codes. Cambridge, U.K.: Cambridge Univ. Press, 1992.
3. A. Baliga, New self-dual codes from cocyclic Hadamard matrices, J. Combin. Math. Combin. Comp., vol. 28, pp. 237-248, 1998.
4. _, Cocyclic Codes of Length 40, 1999. Preprint.
5. 2 Australas. J. Combin., vol. 11, pp. 123-134, 1995.
6. 4, IEEE Trans. Inform. Theory, vol. 43, pp. 1-13, Jan. 1997.
7. S. Boztaş, Constacyclic codes and constacyclic DFTs, in Proc. IEEE Int. Symp. Information Theory, Cambridge, MA, Aug. 1998, p. 235.
8. C. J. Colbourn and J. H. Dinitz, Eds., The CRC Handbook of Combinatorial Designs. Boca Raton, FL: CRC, 1996.
9. Y. Q. Chen, On the existence of abelian Hadamard difference sets and a new family of difference sets, Finite Fields Appl., vol. 3, pp. 234-256, 1997.
10. W. de Launey and M. Smith, Cocyclic Orthogonal Designs and the Asymptotic Existence of Maximal Size Relative Difference Sets with Forbidden Subgroup Size 2, 1998. Preprint.
11. 4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, vol. 40, pp. 301-319, Mar. 1994.
12. K. J. Horadam and A. A. I. Perera, Codes from cocycles, in Proc. AAECC-12 (Lecture Notes in Computer Science), T. Mora and H. Mattson, Eds. Berlin, Germany: Springer-Verlag, 1997, vol. 1255, pp. 151-163.
13. a, 1)-Difference Sets, 1999. Preprint.
14. G. Hughes, Constacyclic codes and cocycles, in Proc. IEEE Int. Symp. Information Theory , Cambridge, MA, Aug. 1998, p. 233.
15. N. Ito, On Hadamard groups, J. Algebra, vol. 168, pp. 981-987, 1994.
16. J. Jedwab, Generalized perfect arrays and Menon difference sets, Des., Codes Cryptogr., vol. 2, pp. 19-68, 1992.
17. P. V. Kumar, On the existence of square dot-matrix patterns having a specific three-valued periodic-correlation function, IEEE Trans. Inform. Theory, vol. 34, pp. 271-277, Mar. 1988.
18. C. Mackenzie and J. Seberry, Maximal q-ary codes and Plotkin's bound, Ars Combin., vol. 26B, pp. 37-50, 1988.
19. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1996. 9th ed.
20. A. A. I. Perera and K. J. Horadam, Cocyclic generalized Hadamard matrices and central relative difference sets, Des., Codes Cryptogr., vol. 15, pp. 187-200, 1998.
21. A. Pott, Finite Geometry and Character Theory (Lecture Notes in Mathematics). Berlin, Germany: Springer-Verlag, 1995, vol. 1601.
22. V. D. Tonchev, Self-orthogonal designs and extremal doubly even codes, J. Combin. Theory Ser. A, vol. 52, pp. 197-205, 1989.
23. R. J. Turyn, An infinite class of Williamson matrices, J. Combin. Theory Ser. A, vol. 12, pp. 319-321, 1972.