The extended and generalized rank weight enumerator of a code

R.P.M.J. Jurrius; G.R. Pellikaan

The extended and generalized rank weight enumerator of a code

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

Samenvatting

This paper investigates the rank weight enumerator of a code over L, where L is a finite extension of a field K. This is a generalization of the case where K = F_q and L = F_{q^m} of Gabidulin codes to arbitrary characteristic. We use the notion of counting polynomials, to define the (extended) rank weight enumerator, since in this generality the set of codewords of a given rank weight is no longer finite. Also the extended and generalized rank weight enumerator are studied in analogy with previous work on codes with respect to the Hamming metric.

Originele taal-2	Engels
Titel	Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014)
Redacteuren	E. Martínez-Moro, I. Kotsireas, S. Szabo
Plaats van productie	Valladolid
Uitgeverij	University of Valladolid
Pagina's	1-5
Status	Gepubliceerd - 2014
Evenement	conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12 - Duur: 9 jul. 2014 → 12 jul. 2014

Congres

Congres	conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12
Periode	9/07/14 → 12/07/14
Ander	20th Conference on Applications of Computer Algebra

Citeer dit

Jurrius, R. P. M. J., & Pellikaan, G. R. (2014). The extended and generalized rank weight enumerator of a code. In E. Martínez-Moro, I. Kotsireas, & S. Szabo (editors), Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014) (blz. 1-5). University of Valladolid.

Jurrius, R.P.M.J. ; Pellikaan, G.R. / The extended and generalized rank weight enumerator of a code. Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014). redacteur / E. Martínez-Moro ; I. Kotsireas ; S. Szabo. Valladolid : University of Valladolid, 2014. blz. 1-5

@inproceedings{0f5d00c579c94557bbd8c685e807dd31,

title = "The extended and generalized rank weight enumerator of a code",

abstract = "This paper investigates the rank weight enumerator of a code over L, where L is a finite extension of a field K. This is a generalization of the case where K = F_q and L = F_{q^m} of Gabidulin codes to arbitrary characteristic. We use the notion of counting polynomials, to define the (extended) rank weight enumerator, since in this generality the set of codewords of a given rank weight is no longer finite. Also the extended and generalized rank weight enumerator are studied in analogy with previous work on codes with respect to the Hamming metric.",

author = "R.P.M.J. Jurrius and G.R. Pellikaan",

year = "2014",

language = "English",

pages = "1--5",

editor = "E. Mart{\'i}nez-Moro and I. Kotsireas and S. Szabo",

booktitle = "Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014)",

publisher = "University of Valladolid",

note = "conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12 ; Conference date: 09-07-2014 Through 12-07-2014",

}

Jurrius, RPMJ & Pellikaan, GR 2014, The extended and generalized rank weight enumerator of a code. in E Martínez-Moro, I Kotsireas & S Szabo (uitgave), Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014). University of Valladolid, Valladolid, blz. 1-5, conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12, 9/07/14.

The extended and generalized rank weight enumerator of a code. / Jurrius, R.P.M.J.; Pellikaan, G.R.
Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014). uitgave / E. Martínez-Moro; I. Kotsireas; S. Szabo. Valladolid: University of Valladolid, 2014. blz. 1-5.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

TY - GEN

T1 - The extended and generalized rank weight enumerator of a code

AU - Jurrius, R.P.M.J.

AU - Pellikaan, G.R.

PY - 2014

Y1 - 2014

N2 - This paper investigates the rank weight enumerator of a code over L, where L is a finite extension of a field K. This is a generalization of the case where K = F_q and L = F_{q^m} of Gabidulin codes to arbitrary characteristic. We use the notion of counting polynomials, to define the (extended) rank weight enumerator, since in this generality the set of codewords of a given rank weight is no longer finite. Also the extended and generalized rank weight enumerator are studied in analogy with previous work on codes with respect to the Hamming metric.

AB - This paper investigates the rank weight enumerator of a code over L, where L is a finite extension of a field K. This is a generalization of the case where K = F_q and L = F_{q^m} of Gabidulin codes to arbitrary characteristic. We use the notion of counting polynomials, to define the (extended) rank weight enumerator, since in this generality the set of codewords of a given rank weight is no longer finite. Also the extended and generalized rank weight enumerator are studied in analogy with previous work on codes with respect to the Hamming metric.

M3 - Conference contribution

SP - 1

EP - 5

BT - Computer Algebra in Coding Theory and Cryptography (Special Session at 20th Conference on Applications of Computer Algebra, ACA 2014, New York NY, USA, July 9-12, 2014)

A2 - Martínez-Moro, E.

A2 - Kotsireas, I.

A2 - Szabo, S.

PB - University of Valladolid

CY - Valladolid

T2 - conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12

Y2 - 9 July 2014 through 12 July 2014

ER -

The extended and generalized rank weight enumerator of a code

Samenvatting

Congres

Vingerafdruk

Citeer dit