메뉴 건너뛰기




Volumn 57, Issue 4, 2007, Pages 1051-1062

On the construction of dense Lattices with a given automorphisms group

Author keywords

Automorphism group; Double circulant codes; Lattice packings; Minkowski Hlawka lower bound; Probability

Indexed keywords


EID: 34547470406     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.2286     Document Type: Article
Times cited : (17)

References (11)
  • 1
    • 85039234445 scopus 로고    scopus 로고
    • A new inequality for the Hermite constants
    • arXiv:math.NT/0603477
    • R. BACHER, "A new inequality for the Hermite constants", arXiv:math.NT/0603477, 2006.
    • (2006)
    • BACHER, R.1
  • 2
    • 84963012034 scopus 로고
    • A lower bound for the optimal density of lattice packings
    • K. BALL, "A lower bound for the optimal density of lattice packings", Internat. Math. Res. Notices 10 (1992), p. 217-221.
    • (1992) Internat. Math. Res. Notices , vol.10 , pp. 217-221
    • BALL, K.1
  • 4
    • 4544360025 scopus 로고
    • Hlawka's theorem in the geometry of numbers
    • H. DAVENPORT & C. A. ROGERS, "Hlawka's theorem in the geometry of numbers", Duke Math. J. 14 (1947), p. 367-375.
    • (1947) Duke Math. J , vol.14 , pp. 367-375
    • DAVENPORT, H.1    ROGERS, C.A.2
  • 5
    • 34547440660 scopus 로고    scopus 로고
    • Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
    • P. GABORIT & G. ZÉMOR, "Asymptotic improvement of the Gilbert-Varshamov bound for linear codes", in Inter. Symp. Inf. Theo., ISIT 2006, Seattle, 2006, p. 287-291.
    • (2006) Inter. Symp. Inf. Theo., ISIT 2006, Seattle , pp. 287-291
    • GABORIT, P.1    ZÉMOR, G.2
  • 6
    • 84963042409 scopus 로고
    • Zero-free regions for Dirichlet L-functions and the least prime in an arithmetic progression
    • D. R. HEATH-BROWN, "Zero-free regions for Dirichlet L-functions and the least prime in an arithmetic progression", Proc. London Math. Soc. (3) 64 (1992), no. 2, p. 265-338.
    • (1992) Proc. London Math. Soc. (3) , vol.64 , Issue.2 , pp. 265-338
    • HEATH-BROWN, D.R.1
  • 7
    • 4544375373 scopus 로고    scopus 로고
    • A lower bound on the density of sphere packings via graph theory
    • M. KRIVELEVICH, S. LITSYN &, A. VARDY, "A lower bound on the density of sphere packings via graph theory", Int. Math. Res. Not. (2004), no. 43, p. 2271-2279.
    • (2004) Int. Math. Res. Not , Issue.43 , pp. 2271-2279
    • KRIVELEVICH, M.1    LITSYN, S.2    VARDY, A.3
  • 8
    • 4544266195 scopus 로고
    • Existence theorems in the geometry of numbers
    • C. A. ROGERS, "Existence theorems in the geometry of numbers", Ann. of Math. (2) 48 (1947), p. 994-1002.
    • (1947) Ann. of Math. (2) , vol.48 , pp. 994-1002
    • ROGERS, C.A.1
  • 9
    • 33746373879 scopus 로고    scopus 로고
    • J. A. RUSH, A lower bound on packing density, invent. Math 98 (1989), no. 3, p. 499-509.
    • J. A. RUSH, "A lower bound on packing density", invent. Math 98 (1989), no. 3, p. 499-509.
  • 10
    • 84975974390 scopus 로고
    • An improvement to the Minkowski-Hlawka bound for packing superballs
    • J. A. RUSH & N. J. A. SLOANE, "An improvement to the Minkowski-Hlawka bound for packing superballs", Mathematika 34 (1987), no. 1, p. 8-18.
    • (1987) Mathematika , vol.34 , Issue.1 , pp. 8-18
    • RUSH, J.A.1    SLOANE, N.J.A.2
  • 11
    • 31344448427 scopus 로고    scopus 로고
    • Random lattices and random sphere packings: Typical properties
    • S. SHLOSMAN & M. TSFASMAN, "Random lattices and random sphere packings: typical properties", Mose. Math. J. 1 (2001), no. 1, p. 73-89.
    • (2001) Mose. Math. J , vol.1 , Issue.1 , pp. 73-89
    • SHLOSMAN, S.1    TSFASMAN, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.