Affine Grassmann codes

Tom Høholdt; Peter Beelen; Sudhir Ramakant Ghorpade

doi:10.1109/TIT.2010.2048470

Affine Grassmann codes

Tom Høholdt
, Peter Beelen
, Sudhir Ramakant Ghorpade

Indian Institute of Technology Bombay

Research output: Contribution to journal › Journal article › Research › peer-review

Abstract

We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes.We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.

Original language	English
Journal	I E E E Transactions on Information Theory
Volume	56
Issue number	7
Pages (from-to)	3166-3176
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2010.2048470
Publication status	Published - 2010

Keywords

Grassmann codes
Automorphism group
Number of minimum weight codewords

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10.1109/TIT.2010.2048470

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title = "Affine Grassmann codes",

abstract = "We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes.We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.",

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year = "2010",

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language = "English",

volume = "56",

pages = "3166--3176",

journal = "I E E E Transactions on Information Theory",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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TY - JOUR

T1 - Affine Grassmann codes

AU - Høholdt, Tom

AU - Beelen, Peter

AU - Ghorpade, Sudhir Ramakant

PY - 2010

Y1 - 2010

N2 - We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes.We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.

AB - We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes.We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.

KW - Grassmann codes

KW - Automorphism group

KW - Number of minimum weight codewords

U2 - 10.1109/TIT.2010.2048470

DO - 10.1109/TIT.2010.2048470

M3 - Journal article

SN - 0018-9448

VL - 56

SP - 3166

EP - 3176

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

IS - 7

ER -

Affine Grassmann codes

Abstract

Keywords

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