zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Applications of coding theory to the construction of modular lattices. (English) Zbl 0876.94053
The author studies codes obtained by starting with a maximal order $D$ in $K$ which is either an imaginary quadratic field, or a quaternion field with center $Q$ ramified at infinity and taking a left submodule in $(d/pD)^n$. She obtains general bounds for these codes and constructs some extremal self-dual codes.

94B99Theory of error-correcting codes and error-detecting codes
06C05Modular lattices, Desarguesian lattices
Full Text: DOI
[1] Assmus, E. F.; Mattson, H. F.: New 5-designs. J. combin. Theory 6, 122-151 (1969) · Zbl 0179.02901
[2] Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A.: ATLAS of finite groups. (1985) · Zbl 0568.20001
[3] Bachoc, C.: Voisinages au sens de kesner pour LES réseaux quaternioniens. Comm. math. Helvet. 70, 350-374 (1995)
[4] C. Batut, H.-G. Quebbeman, R. Scharlau, Computations of cyclotomic lattices, Exp. Math. · Zbl 0873.11026
[5] Conway, J. H.; Pless, V.; Sloane, N. J. A.: Self-dual codes overgfgf. IEEE trans. Inform. theory 25, 312-322 (1979) · Zbl 0401.94025
[6] Conway, J. H.; Sloane, N. J. A.: Sphere packings, lattices and groups. (1988) · Zbl 0634.52002
[7] Conway, J. H.; Sloane, N. J. A.: The Coxeter--Todd lattice, the mitchell group, and related sphere packings. Math. proc. Cambridge phil. Soc. 93, 421-440 (1983) · Zbl 0518.10035
[8] J. H. Conway, N. J. A. Sloane, 1993, Self-dual codes over the integers modulo 4, 62, 30, 45 · Zbl 0763.94018
[9] P. Delsarte, An algebraic approach to the association schemes of coding theory, Philips Res. Rep. Suppl
[10] Feit, W.: Some lattices $overQ(-3)$. J. algebra 52, 248-263 (1978) · Zbl 0377.10018
[11] P. Gaborit, Mass formula for self-dual codes over Z4q+uqrings
[12] Macwilliams, F. J.; Odlysko, A. M.; Sloane, N. J. A.: Self-dual codes over F4. J. combin. Theory ser. A 25, 288-318 (1978) · Zbl 0397.94013
[13] Mallows, C. L.; Odlysko, A. M.; Sloane, N. J. A.: Upper bounds for modular forms, lattices and codes. J. algebra 36, 68-76 (1975) · Zbl 0311.94002
[14] Macwilliams, F. J.; Sloane, N. J. A.: The theory of error-correcting codes. (1977) · Zbl 0369.94008
[15] J. Martinet, 1995, Structures algébriques sur les réseaux, Number Theory, S. David, Séminaire de Théorie des Nombres de Paris, 1992--93, Cambridge Univ. Press, Cambridge
[16] J. Martinet, Les réseaux parfaits des espaces euclidiens
[17] Nebe, G.: Endliche rationale matrixgruppen vom Grad 24, aachener beiträge zur Mathematik. (1995)
[18] G. Nebe, Finite subgroups ofGln(Q) for 25\leqslantn, Comm. Algebra
[19] Nebe, G.; Plesken, W.: Finite rational matrix groups. Mem. am. Math. soc. 116, 556 (1995) · Zbl 0837.20056
[20] Quebbemann, H. -G.: An application of Siegel’s formula over quaternion orders. Mathematika 31, 12-16 (1984) · Zbl 0538.10027
[21] Quebbemann, H. -G.: A construction of integral lattices. Mathematika 31, 138-141 (1984) · Zbl 0538.10028
[22] Quebbemann, H. -G.: Lattices with theta-functions forg2). J. algebra 105, 443-450 (1987) · Zbl 0609.10026
[23] Quebbemann, H. -G.: Modular lattices in Euclidean spaces. J. number theory 54, 190-202 (1995) · Zbl 0874.11038
[24] Sloane, N. J. A.: Error-correcting codes and invariant theory: new applications of nineteenth century technique. Amer. math. Monthly 84, 82-107 (1977) · Zbl 0357.94014
[25] R. Scharlau, B. Hemkemeier, Classification of integral lattices with large class number · Zbl 0919.11031
[26] Vigneras, M. -F.: Arithmétique des algèbres de quaternions. Lecture notes in mathematics 800 (1980)