Coding-theoretic constructions for (t,m,s)-nets and ordered orthogonal arrays

Journal of Combinatorial Designs

Volumn 10, Issue 6, 2002, Pages 403-418

  Bierbrauer, Jürgen ^a   Edel, Yves ^b   Schmid, Wolfgang Ch ^c  

^a MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

^b UNIVERSITY OF HEIDELBERG   (Germany)

^c UNIVERSITY OF SALZBURG   (Austria)

Author keywords

(T; (U; Concatenation; Distance; Duality; Error correcting codes; Gilbert varshamov bound; M; Nrt space; Ordered orthogonal arrays; Quasi monte carlo methods; S ) nets; Strength; U + v) bound

Indexed keywords

(T; CONCATENATION; DISTANCE; DUALITY; ERROR CORRECTING CODE; GILBERT-VARSHAMOV BOUND; M; NRT SPACE; ORDERED ORTHOGONAL ARRAY; QUASI MONTE CARLO METHODS; S )-NETS; STRENGTH;

COMPUTER PROGRAMMING; GEOMETRY; MONTE CARLO METHODS;

INFORMATION THEORY;

EID: 3142724271     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.10015     Document Type: Article

References (27)

1. J. Bierbrauer and Y. Edel, Lengthening and the Gilbert-Varshamov bound, IEEE Trans. Inform. Theory 43 (1997), 991-992. (Pubitemid 127828020)
2. J. Bierbrauer and Y. Edel, Construction of digital nets from BCH-codes, Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics 127 (1997), 221-231.
3. A. E. Brouwer, Data base of bounds for the minimum distance for linear codes, (http://www.win.tue.nl/aeb/voorlincod.html).
4. W. W. L. Chen, M. M. Skriganov, Explicit constructions in the classical mean squares problem in irregularities of point distributions 545 (2002), 67-95, J Reine Angewandte Math. (Pubitemid 36932381)
5. A. T. Clayman, K. M. Lawrence, G. L. Mullen, H. Niederreiter, N. J. A. Sloane, Updated tables of parameters of ot;m; s-nets, J Combin Designs 7 (1999), 381-393.
6. I. Dumer, V. A. Zinoviev, Some new maximal codes over GF(4), Probl Peredach Inform 14 (1978), 24-34, translation in Problems in Information Transmission 1979, 174-181. (Pubitemid 9463871)
7. Y. Edel, Extensions of generalized product caps, Designs, Codes and Cryptography (in press).
8. Y. Edel, J. Bierbrauer, Families of ternary ot;m; s-nets related to BCH-codes, Monatsh Math 132 (2001), 99-103. (Pubitemid 33576437)
9. Y. Edel, J. Bierbrauer, Large caps in small spaces, Designs, Codes and Cryptography 23 (2001), 197-212. (Pubitemid 33672832)
10. D. N. Gevorkyan, A. M. Avetisyan, G. A. Tigranyan, On the structure of two-errorcorrecting in Hamming metric over Galois fields, In: Computational Techniques (in Russian) 3, Kuibyshev 1975, 19-21.
11. K. M. Lawrence, A combinatorial characterization of ot;m; s-nets in base b, J Combin Designs 4 (1996), 275-293. (Pubitemid 126606819)
12. K. M. Lawrence, Construction of ot;m; s-nets and orthogonal arrays from binary codes, manuscript.
13. F. J. McWilliams, N. J. Sloane, The theory of error-correcting codes, North-Holland, Amsterdam 1977.
14. W. J. Martin, D. R. Stinson, Association schemes for ordered orthogonal arrays and (t,m,s)-nets, Canadian Journal of Mathematics 51(1999), 326-346.
15. G. L. Mullen, W. Ch. Schmid, An equivalence between ot;m; s-nets and strongly orthogonal hypercubes, J Combin Theory A 76 (1996), 164-174.
16. H. Niederreiter, Low-discrepancy point sets, Monatsh Math 102 (1986), 155-167.
17. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
18. H. Niederreiter, A statistical analysis of generalized feedback shift register pseudorandom number generators, SIAM J Sci Statist Comp 8 (1987), 1035-1051.
19. H. Niederreiter, Constructions of ot;m; s-nets,Monte Carlo and Quasi-Monte Carlo Methods 1998, (H. Niederreiter and J. Spanier, eds), Springer, Berlin (2000), 70-85.
20. H. Niederreiter, G. Pirsic, Duality for digital nets and its applications, Acta Arith 97 (2001), 173-182.
21. H. Niederreiter, G. Pirsic, A Kronecker product construction for digital nets, Monte Carlo and Quasi-Monte Carlo Methods 2000, (K. T. Fang, F. J. Hickernell and H. Niederreiter, eds), Springer, Berlin (2002), 396-405.
22. H. Niederreiter, C. P. Xing: Nets, ot; ssequences, and algebraic geometry, Random and Quasi-Random Point Sets (P. Hellekalek and G. Larcher, eds), Lecture Notes in Statistics 138 (1998), 267-302.
23. M. Yu. Rosenbloom, M. A. Tsfasman, Codes for the m-metric, Problems of information transmission 33 (1997), 45-52, translated fromProblemy Peredachi Informatsii 33 (1996), 55-63.
24. W. Ch. Schmid, ot;m; s-nets: Digital construction and combinatorial aspects, PhD dissertation, Salzburg (Austria), 1995.
25. W. Ch. Schmid, R. Wolf, Bounds for digital nets and sequences, Acta Arith. 78 (1997), 377-399. (Pubitemid 127176949)
26. N. J. A. Sloane, D. S. Whitehead, A new family of single-error correcting codes, IEEE Trans Inform Theory 16 (1970), 717-719.
27. M. M. Skriganov, Coding theory and uniform distributions, 13 (2002), 301-337 St. Petersburg Math J, translated from Algebra i Analiz 13 (2001), 191-239.