Lattices invariant under the affine general linear group

Kanat Abdukhalikov

doi:10.1016/S0021-8693(03)00496-4

Lattices invariant under the affine general linear group

Kanat Abdukhalikov

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Integral lattices invariant under the affine group AGL_m (p^t) in its natural permutation module Λ of dimension n = mt are studied. A complete description of such lattices is given. As a consequence we have results on automorphism groups of affine invariant codes over fields and finite residue rings ℤ/p^kℤ.

Original language	English
Pages (from-to)	638-662
Number of pages	25
Journal	Journal of Algebra
Volume	276
Issue number	2
DOIs	https://doi.org/10.1016/S0021-8693(03)00496-4
Publication status	Published - Jun 15 2004
Externally published	Yes

Keywords

Automorphism groups
Cyclic codes
Lattices

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0021-8693(03)00496-4

Cite this

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title = "Lattices invariant under the affine general linear group",

abstract = "Integral lattices invariant under the affine group AGLm (pt) in its natural permutation module Λ of dimension n = mt are studied. A complete description of such lattices is given. As a consequence we have results on automorphism groups of affine invariant codes over fields and finite residue rings ℤ/pkℤ.",

keywords = "Automorphism groups, Cyclic codes, Lattices",

author = "Kanat Abdukhalikov",

year = "2004",

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T1 - Lattices invariant under the affine general linear group

AU - Abdukhalikov, Kanat

PY - 2004/6/15

Y1 - 2004/6/15

N2 - Integral lattices invariant under the affine group AGLm (pt) in its natural permutation module Λ of dimension n = mt are studied. A complete description of such lattices is given. As a consequence we have results on automorphism groups of affine invariant codes over fields and finite residue rings ℤ/pkℤ.

AB - Integral lattices invariant under the affine group AGLm (pt) in its natural permutation module Λ of dimension n = mt are studied. A complete description of such lattices is given. As a consequence we have results on automorphism groups of affine invariant codes over fields and finite residue rings ℤ/pkℤ.

KW - Automorphism groups

KW - Cyclic codes

KW - Lattices

UR - http://www.scopus.com/inward/record.url?scp=2942670594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942670594&partnerID=8YFLogxK

U2 - 10.1016/S0021-8693(03)00496-4

DO - 10.1016/S0021-8693(03)00496-4

M3 - Article

AN - SCOPUS:2942670594

SN - 0021-8693

VL - 276

SP - 638

EP - 662

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Lattices invariant under the affine general linear group

Abstract

Keywords

ASJC Scopus subject areas

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