Hypercubic 4 and 5-designs from double-error-correcting BCH codes

Designs, Codes, and Cryptography

Volumn 28, Issue 3, 2003, Pages 265-282

  Helleseth, Tor ^a   Kløve, Torleiv ^a   Levenshtein, Vladimir I ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

Author keywords

BCH codes; designs; orthogonal arrays

Indexed keywords

EID: 84867923529     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024110021836     Document Type: Article

References (14)

1. R. C. Bose 1947 Mathematical theory of the symmetrical factorial design Sankhya 8 128 139
2. Y. Edel and J. Bierbrauer, Construction of digital nets from BCH codes, In (H. Niederreiter et al., eds.), Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics, Vol. 127, Springer (1998) pp. 221-231.
3. G. Lachaud J. Wolfmann 1990 The weights of the orthogonals of the extended quadratic binary Goppa codes IEEE Trans. on Inform. Theory 36 686 692
4. K. M. Lawrence 1996 A combinatorial interpretation of (t, m, s)-nets in base b Journal of Combinatorial Designs 4 275 293
5. K. M. Lawrence, A. Mahalanabis, G. L. Mullen and W. C. Schmid, Construction of digital (t,m, s)-nets from linear codes, In (S. D. Cohen and H. Niederreiter, eds.), Finite Fields and Applications, Lect. Note Series of the London Math. Soc., Vol. 233, Camb. Univ. Press, Cambridge (1996) pp. 189-208.
6. V. I. Levenshtein 1997 Split orthogonal arrays and maximum independent resilient systems of functions Designs, Codes and Cryptography 12 2 131 160
7. W. J. Martin D. R. Stinson 1999 A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets Canad. Math. Bull. 42 3 359 370
8. W. J. Martin D. R. Stinson 1999 Association schemes for ordered orthogonal arrays and (t, m, s)-nets Canad. J. Math. 51 2 326 346
9. C. Moreno O. Moreno 1991 Exponential sums and Goppa codes: I Proc. Amer. Math. Soc. 111 2 523 531
10. G. L. Mullen W. C. Schmid 1996 An equivalence between (t, m, s)-nets and strongly orthogonal hypercubes Journal of Combinatorial Theory, Ser. A 76 164 174
11. H. Niederreiter 1987 Point sets and sequences with small discrepancy Monatsh. Math. 104 273 337
12. C. R. Rao 1947 Factorial experiments derivable from combinatorial arrangements of arrays J. R. Stat. Soc. 89 128 139
13. M. J. Rozenblyum M. A. Tsfasman 1977 Codes for m-metric Problemy Peredachi Inform. 33 1 55 63 English translation in Problems of Inform. Trans., Vol. 33, No. 1 (1977) pp. 45- 52
14. I. M. Sobol' 1967 Distribution of points in a cube and the approximate evaluation of integrals Zh. Vychisl. Mat. i Mat. Fiz. 7 784 802 English translation in USSR Comput. Math. Math. Phys., Vol. 7 (1967) pp. 86- 112