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Algebra i Analiz, 2001, Volume 13, Issue 2, Pages 191–239 (Mi aa932)  

This article is cited in 46 scientific papers (total in 46 papers)

Research Papers

Coding theory and uniform distributions

M. M. Skriganov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full text: PDF file (2374 kB)

English version:
St. Petersburg Mathematical Journal, 2002, 13:2, 301–337

Bibliographic databases:
Received: 23.08.2000

Citation: M. M. Skriganov, “Coding theory and uniform distributions”, Algebra i Analiz, 13:2 (2001), 191–239; St. Petersburg Math. J., 13:2 (2002), 301–337

Citation in format AMSBIB
\Bibitem{Skr01}
\by M.~M.~Skriganov
\paper Coding theory and uniform distributions
\jour Algebra i Analiz
\yr 2001
\vol 13
\issue 2
\pages 191--239
\mathnet{http://mi.mathnet.ru/aa932}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1834866}
\zmath{https://zbmath.org/?q=an:0994.11028}
\transl
\jour St. Petersburg Math. J.
\yr 2002
\vol 13
\issue 2
\pages 301--337


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. T. Dougherty, M. M. Skriganov, “MacWilliams duality and the Rosenbloom–Tsfasman metric”, Mosc. Math. J., 2:1 (2002), 81–97  mathnet  mathscinet  zmath
    2. Bierbrauer J., Edel Y., Schmid W. Ch., “Coding-theoretic constructions for $(t,m,s)$-nets and ordered orthogonal arrays”, J. Combin. Des., 10:6 (2002), 403–418  crossref  mathscinet  zmath  isi  scopus
    3. Niederreiter H., Ozbudak F., “Constructions of digital nets using global function fields”, Acta Arithmetica, 105:3 (2002), 279–302  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Hellekalek P., “Digital (t, m, s)–nets and the spectral test”, Acta Arithmetica, 105:2 (2002), 197–204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Dougherty S.T., Skriganov M.M., “Maximum distance separable codes in the rho metric over arbitrary alphabets”, Journal of Algebraic Combinatorics, 16:1 (2002), 71–81  crossref  mathscinet  zmath  isi
    6. Lee Kwankyu, “The automorphism group of a linear space with the Rosenbloom-Tsfasman metric”, European J. Combin., 24:6 (2003), 607–612  crossref  mathscinet  zmath  isi  scopus
    7. Dougherty S. T., Shiromoto K., “Maximum distance codes in $\mathrm{Mat}_{n,s}(\mathbb Z_k)$ with a non-hamming metric and uniform distributions”, Des. Codes Cryptogr., 33:1 (2004), 45–61  crossref  mathscinet  zmath  isi  scopus
    8. Siap I., Ozen M., “The complete weight enumerator for codes over $\mathscr M_{n\times s}(R)$”, Appl. Math. Lett., 17:1 (2004), 65–69  crossref  mathscinet  zmath  isi  scopus
    9. Xing C.P., Niederreiter H., “Digital nets, duality, and algebraic curves”, Monte Carlo and Quasi-Monte Carlo Methods 2002, 2004, 155–166  crossref  mathscinet  zmath  isi
    10. Kim Dae San, “Dual MacWilliams pair”, IEEE Trans. Inform. Theory, 51:8 (2005), 2901–2905  crossref  mathscinet  zmath  isi  scopus
    11. Kim Hyun Kwang, Oh Dong Yeol, “A classification of posets admitting the MacWilliams identity”, IEEE Trans. Inform. Theory, 51:4 (2005), 1424–1431  crossref  mathscinet  zmath  isi  scopus
    12. Niederreiter H., “Constructions of (t, m, s)–nets and (t, s)–sequences”, Finite Fields and Their Applications, 11:3 (2005), 578–600  crossref  mathscinet  zmath  isi  scopus
    13. Skriganov M. M., “Harmonic analysis on totally disconnected groups and irregularities of point distributions”, J. Reine Angew. Math., 600 (2006), 25–49  crossref  mathscinet  zmath  isi  elib  scopus
    14. Cho Sung Hee, Kim Dae San, “Automorphism group of the crown-weight space”, European J. Combin., 27:1 (2006), 90–100  crossref  mathscinet  zmath  isi  scopus
    15. Ozen M., Siap I., “Linear codes over $\mathbb F_q[u]/(u^s)$ with respect to the Rosenbloom-Tsfasman metric”, Des. Codes Cryptogr., 38:1 (2006), 17–29  crossref  mathscinet  zmath  isi  scopus
    16. Vontobel P.O., Ganesan A., “On universally decodable matrices for space–time coding”, Designs Codes and Cryptography, 41:3 (2006), 325–342  crossref  mathscinet  zmath  isi  scopus
    17. Skriganov M. M., “On linear codes with large weights simultaneously for the Rosenbloom-Tsfasman and Hamming metrics”, J. Complexity, 23:4-6 (2007), 926-936  crossref  mathscinet  zmath  isi  elib  scopus
    18. Quistoff J., “On Rosenbloom and Tsfasman's generalization of the hamming space”, Discrete Math., 307:21 (2007), 2514–2524  crossref  mathscinet  isi  scopus
    19. Ozen M., Siap I., “Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric”, J. Franklin Inst., 344:5 (2007), 790–799  crossref  mathscinet  zmath  isi  scopus
    20. Kim Dae San, “MacWilliams-type identities for fragment and sphere enumerators”, European J. Combin., 28:1 (2007), 273–302  crossref  mathscinet  zmath  isi  scopus
    21. Hyun Jong Yoon, Kim Hyun Kwang, “Maximum distance separable poset codes”, Des. Codes Cryptogr., 48:3 (2008), 247–261  crossref  mathscinet  zmath  isi  scopus
    22. Chen W.W.L., Skriganov M.M., “Orthogonality and digit shifts in the classical mean squares problem in irregularities of point distribution”, Diophantine Approximation - Festschrift for Wolfgang Schmidt, Developments in Mathematics, 16, 2008, 141–159  crossref  mathscinet  zmath  isi  scopus
    23. Alexander Barg, Punabrasu Purkayastha, “Bounds on ordered codes and orthogonal arrays”, Mosc. Math. J., 9:2 (2009), 211–243  mathnet  mathscinet  zmath
    24. Hellekalek P., “A general discrepancy estimate based on $p$-adic arithmetics”, Acta Arith., 139:2 (2009), 117–129  crossref  mathscinet  zmath  adsnasa  isi  scopus
    25. Schuerer R., Schmid W.Ch., “MINT – New Features and New Results”, Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, 171–189  crossref  mathscinet  zmath  isi
    26. Hellekalek P., “A notion of diaphony based on p-adic arithmetic”, Acta Arithmetica, 145:3 (2010), 273–284  crossref  mathscinet  zmath  isi  scopus
    27. Hyun J.Y., “A Subgroup of the Full Poset-Isometry Group”, SIAM Journal on Discrete Mathematics, 24:2 (2010), 589–599  crossref  mathscinet  zmath  isi  scopus
    28. Barg A., Purkayastha P., “Near MDS poset codes and distributions”, IEEE International Symposium on Information Theory, 2010, 1310–1314  crossref  isi  scopus
    29. Barg A., Purkayastha P., “Near MDS poset codes and distributions”, Error-Correcting Codes, Finite Geometries and Cryptography, Contemporary Mathematics, 523, 2010, 135–147  crossref  mathscinet  zmath  isi
    30. M. M. Skriganov, “Khinchin's inequality and Chen's theorem”, St. Petersburg Math. J., 23:4 (2012), 761–778  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    31. Hyun J.Y., Lee Y., “MDS Poset-Codes Satisfying the Asymptotic Gilbert-Varshamov Bound in Hamming Weights”, IEEE Trans Inform Theory, 57:12 (2011), 8021–8026  crossref  mathscinet  zmath  isi  elib  scopus
    32. M. M. Skriganov, “On mean values of the $L_q$-discrepancies of point distributions”, St. Petersburg Math. J., 24:6 (2013), 991–1012  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    33. Kim D.S., Kim H.K., “Association Schemes and Macwilliams Dualities for Generalized Niederreiter-Rosenbloom-Tsfasman Posets”, Diss. Math., 2012, no. 487, 5+  mathscinet  isi
    34. Oh D.Y., “Poset Metrics Admitting Association Schemes and a New Proof of Macwilliams Identity”, J. Korean. Math. Soc., 50:5 (2013), 917–931  crossref  mathscinet  zmath  isi  elib  scopus
    35. Matsumoto M., Saito M., Matoba K., “A Computable Figure of Merit For Quasi-Monte Carlo Point Sets”, Math. Comput., 83:287 (2014), 1233–1250  crossref  mathscinet  zmath  isi  elib  scopus
    36. Barg A., Felix L.V., Firer M., Spreafico M.V.P., “Linear Codes on Posets With Extension Property”, Discrete Math., 317 (2014), 1–13  crossref  mathscinet  zmath  isi  elib  scopus
    37. Alexander Barg, Woomyoung Park, “On linear ordered codes”, Mosc. Math. J., 15:4 (2015), 679–702  mathnet  mathscinet
    38. Suzuki K., “Wafom Over Abelian Groups For Quasi-Monte Carlo Point Sets”, Hiroshima Math. J., 45:3 (2015), 341–364  mathscinet  zmath  isi
    39. Castoldi A.G., Monte Carmelo E.L., “the Covering Problem in Rosenbloom-Tsfasman Spaces”, Electron. J. Comb., 22:3 (2015), P3.30  mathscinet  zmath  isi
    40. Dougherty S.T., “Foundations of Algebraic Coding Theory”, Noncommutative Rings and Their Applications, Contemporary Mathematics, 634, eds. Dougherty S., Facchini A., Leroy A., Puczylowski E., Sole P., Amer Mathematical Soc, 2015, 101–136  crossref  mathscinet  zmath  isi
    41. Zhou W., Lin Sh., Abdel-Ghaffar Kh.A.S., “BCH Codes for the Rosenbloom–Tsfasman Metric”, IEEE Trans. Inf. Theory, 62:12 (2016), 6757–6767  crossref  mathscinet  zmath  isi  scopus
    42. Jain S., “Duality in Lp Gamma-Spaces”, ARS Comb., 129 (2016), 107–122  mathscinet  zmath  isi
    43. Jain S., “Error Location Technique in Rt-Spaces”, ARS Comb., 128 (2016), 33–46  mathscinet  zmath  isi
    44. Castoldi A.G., Moura L., Panario D., Stevens B., “Ordered Orthogonal Array Construction Using LFSR Sequences”, IEEE Trans. Inf. Theory, 63:2 (2017), 1336–1347  crossref  mathscinet  zmath  isi  scopus
    45. Marka V., Selvaraj R.S., Gnanasudha I., “Self-Dual Codes in the Rosenbloom-Tsfasman Metric”, Math. Commun., 22:1 (2017), 75–87  mathscinet  zmath  isi
    46. Panario D., Saaltink M., Stevens B., Wevrick D., “A General Construction of Ordered Orthogonal Arrays Using Lfsrs”, IEEE Trans. Inf. Theory, 65:7 (2019), 4316–4326  crossref  isi
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