On codes over rings invariant under affine groups

Kanat Abdukhalikov

doi:10.3934/amc.2013.7.253

On codes over rings invariant under affine groups

Kanat Abdukhalikov

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

1 Citation (Scopus)

Abstract

We give a description of extended cyclic codes of length pⁿ over a field and over the ring of integers modulo p^e admitting the affine group AGL_m(p^t), n = mt, as a permutation group.

Original language	English
Pages (from-to)	253-265
Number of pages	13
Journal	Advances in Mathematics of Communications
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/amc.2013.7.253
Publication status	Published - Aug 2013
Externally published	Yes

Keywords

Affine groups
Affine invariant codes
Automorphism groups
Cyclic codes
Defining sets
Extended cyclic codes
Permutation groups

ASJC Scopus subject areas

Algebra and Number Theory
Computer Networks and Communications
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/amc.2013.7.253

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title = "On codes over rings invariant under affine groups",

abstract = "We give a description of extended cyclic codes of length pn over a field and over the ring of integers modulo pe admitting the affine group AGLm(pt), n = mt, as a permutation group.",

keywords = "Affine groups, Affine invariant codes, Automorphism groups, Cyclic codes, Defining sets, Extended cyclic codes, Permutation groups",

author = "Kanat Abdukhalikov",

year = "2013",

month = aug,

doi = "10.3934/amc.2013.7.253",

language = "English",

volume = "7",

pages = "253--265",

journal = "Advances in Mathematics of Communications",

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publisher = "American Institute of Mathematical Sciences",

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N2 - We give a description of extended cyclic codes of length pn over a field and over the ring of integers modulo pe admitting the affine group AGLm(pt), n = mt, as a permutation group.

AB - We give a description of extended cyclic codes of length pn over a field and over the ring of integers modulo pe admitting the affine group AGLm(pt), n = mt, as a permutation group.

KW - Affine groups

KW - Affine invariant codes

KW - Automorphism groups

KW - Cyclic codes

KW - Defining sets

KW - Extended cyclic codes

KW - Permutation groups

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DO - 10.3934/amc.2013.7.253

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SP - 253

EP - 265

JO - Advances in Mathematics of Communications

JF - Advances in Mathematics of Communications

IS - 3

ER -

On codes over rings invariant under affine groups

Abstract

Keywords

ASJC Scopus subject areas

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