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

Access to Document

10.1109/TIT.2010.2048470

OpenUrl availability

Full text

Cite this

@article{38b636200a1c4941be9b88c7025f2b8a,

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.",

keywords = "Grassmann codes, Automorphism group, Number of minimum weight codewords",

author = "Tom H{\o}holdt and Peter Beelen and Ghorpade, {Sudhir Ramakant}",

year = "2010",

doi = "10.1109/TIT.2010.2048470",

language = "English",

volume = "56",

pages = "3166--3176",

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

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers",

number = "7",

}

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

Access to Document

OpenUrl availability

Fingerprint

Cite this