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

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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.

Original language	English
Title of host publication	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)
Editors	E. Martínez-Moro, I. Kotsireas, S. Szabo
Place of Publication	Valladolid
Publisher	University of Valladolid
Pages	1-5
Publication status	Published - 2014
Event	conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12 - Duration: 9 Jul 2014 → 12 Jul 2014

Conference

Conference	conference; 20th Conference on Applications of Computer Algebra; 2014-07-09; 2014-07-12
Period	9/07/14 → 12/07/14
Other	20th Conference on Applications of Computer Algebra

Cite this

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 (Eds.), 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) (pp. 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). editor / E. Martínez-Moro ; I. Kotsireas ; S. Szabo. Valladolid : University of Valladolid, 2014. pp. 1-5

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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\textasciicircum{}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 (eds), 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, pp. 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). ed. / E. Martínez-Moro; I. Kotsireas; S. Szabo. Valladolid: University of Valladolid, 2014. p. 1-5.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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

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