Projective generalized Reed-Muller codes over p-adic numbers and finite rings

Kanat Abdukhalikov

doi:10.1007/978-3-642-56755-1_1

Projective generalized Reed-Muller codes over p-adic numbers and finite rings

Kanat Abdukhalikov

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We consider codes generated over the ring ℤ_p of p-adic integer numbers and the ring ℤ/p^d ℤ of integers modulo p^d by incidence vectors of the designs of points and projective subspaces of a projective space PG(m−1, F_p) , where F_p is a finite field of p elements. Codes invariant under the natural action of the projective group PGL_m(F_p) are described.

Original language	English
Title of host publication	Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, 1-13
Editors	Dieter Jungnickel, Harald Niederreiter
Publisher	Springer, Berlin
ISBN (Print)	978-3-642-62498-8
DOIs	https://doi.org/10.1007/978-3-642-56755-1_1
Publication status	Published - 2001
Event	Finite fields and applications - Augsburg Duration: Aug 1 1999 → …

Conference

Conference	Finite fields and applications
Period	8/1/99 → …

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10.1007/978-3-642-56755-1_1

http://link.springer.com/chapter/10.1007/978-3-642-56755-1_1

Cite this

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title = "Projective generalized Reed-Muller codes over p-adic numbers and finite rings",

abstract = "We consider codes generated over the ring ℤ\_p of p-adic integer numbers and the ring ℤ/p\textasciicircum{}d ℤ of integers modulo p\textasciicircum{}d by incidence vectors of the designs of points and projective subspaces of a projective space PG(m−1, F\_p) , where F\_p is a finite field of p elements. Codes invariant under the natural action of the projective group PGL\_m(F\_p) are described.",

author = "Kanat Abdukhalikov",

year = "2001",

doi = "10.1007/978-3-642-56755-1\_1",

language = "English",

isbn = "978-3-642-62498-8",

editor = "Dieter Jungnickel and Harald Niederreiter",

booktitle = "Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, 1-13",

publisher = "Springer, Berlin",

note = "Finite fields and applications ; Conference date: 01-08-1999",

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N2 - We consider codes generated over the ring ℤ_p of p-adic integer numbers and the ring ℤ/p^d ℤ of integers modulo p^d by incidence vectors of the designs of points and projective subspaces of a projective space PG(m−1, F_p) , where F_p is a finite field of p elements. Codes invariant under the natural action of the projective group PGL_m(F_p) are described.

AB - We consider codes generated over the ring ℤ_p of p-adic integer numbers and the ring ℤ/p^d ℤ of integers modulo p^d by incidence vectors of the designs of points and projective subspaces of a projective space PG(m−1, F_p) , where F_p is a finite field of p elements. Codes invariant under the natural action of the projective group PGL_m(F_p) are described.

U2 - 10.1007/978-3-642-56755-1_1

DO - 10.1007/978-3-642-56755-1_1

M3 - Conference contribution

SN - 978-3-642-62498-8

BT - Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, 1-13

A2 - Jungnickel, Dieter

A2 - Niederreiter, Harald

PB - Springer, Berlin

T2 - Finite fields and applications

Y2 - 1 August 1999

ER -

Projective generalized Reed-Muller codes over p-adic numbers and finite rings

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