Duals of Affine Grassmann Codes and Their Relatives

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Duals of Affine Grassmann Codes and Their Relatives. / Beelen, P.; Ghorpade, S. R.; Hoholdt, T.

In: I E E E Transactions on Information Theory, Vol. 58, No. 6, 2012, p. 3843-3855.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Beelen, P.; Ghorpade, S. R.; Hoholdt, T. / Duals of Affine Grassmann Codes and Their Relatives.

In: I E E E Transactions on Information Theory, Vol. 58, No. 6, 2012, p. 3843-3855.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

Bibtex

@article{618ac625fd9c4628b5b5b34684199e02,
title = "Duals of Affine Grassmann Codes and Their Relatives",
keywords = "Linear codes, Reed-Muller codes, Electronic mail , Frequency modulation, Linear code , Parity check codes, Polynomials, Sparse matrices",
publisher = "I E E E",
author = "P. Beelen and Ghorpade, {S. R.} and T. Hoholdt",
year = "2012",
doi = "10.1109/TIT.2012.2187171",
volume = "58",
number = "6",
pages = "3843--3855",
journal = "I E E E Transactions on Information Theory",
issn = "0018-9448",

}

RIS

TY - JOUR

T1 - Duals of Affine Grassmann Codes and Their Relatives

A1 - Beelen,P.

A1 - Ghorpade,S. R.

A1 - Hoholdt,T.

AU - Beelen,P.

AU - Ghorpade,S. R.

AU - Hoholdt,T.

PB - I E E E

PY - 2012

Y1 - 2012

N2 - Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work by Beelen Here, we consider, more generally, affine Grassmann codes of a given level. We explicitly determine the dual of an affine Grassmann code of any level and compute its minimum distance. Further, we ameliorate the results by Beelen concerning the automorphism group of affine Grassmann codes. Finally, we prove that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords. This provides a clean analogue of a corresponding result for generalized Reed-Muller codes.

AB - Affine Grassmann codes are a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. These codes were introduced in a recent work by Beelen Here, we consider, more generally, affine Grassmann codes of a given level. We explicitly determine the dual of an affine Grassmann code of any level and compute its minimum distance. Further, we ameliorate the results by Beelen concerning the automorphism group of affine Grassmann codes. Finally, we prove that affine Grassmann codes and their duals have the property that they are linear codes generated by their minimum-weight codewords. This provides a clean analogue of a corresponding result for generalized Reed-Muller codes.

KW - Linear codes

KW - Reed-Muller codes

KW - Electronic mail

KW - Frequency modulation

KW - Linear code

KW - Parity check codes

KW - Polynomials

KW - Sparse matrices

U2 - 10.1109/TIT.2012.2187171

DO - 10.1109/TIT.2012.2187171

JO - I E E E Transactions on Information Theory

JF - I E E E Transactions on Information Theory

SN - 0018-9448

IS - 6

VL - 58

SP - 3843

EP - 3855

ER -