Type II codes over IF2r

Koichi Betsumiya; Masaaki Harada; Akihiro Munemasa

Type II codes over IF_2r

Koichi Betsumiya, Masaaki Harada, Akihiro Munemasa

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

Abstract

Motivated by the work of Pasquier and Wolfmann in 1980’s, we define Type II codes over IF2r as self-dual codes with the property that their binary images with respect to a trace-orthogonal basis are doubly-even. We give a classification of Type II codes of length 8 over IF₈, IF₁₆ and IF₃₂. We also characterize all Type II codes whose binary images are the extended Golay [24, 12, 8] code.

Original language	English
Title of host publication	Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings
Editors	Serdar Boztas, Igor E. Shparlinski
Publisher	Springer-Verlag
Pages	102-111
Number of pages	10
ISBN (Print)	9783540456247
Publication status	Published - 2001 Jan 1
Externally published	Yes
Event	14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 2001 - Melbourne, Australia Duration: 2001 Nov 26 → 2001 Nov 30

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2227
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 2001
Country/Territory	Australia
City	Melbourne
Period	01/11/26 → 01/11/30

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Cite this

Betsumiya, K., Harada, M., & Munemasa, A. (2001). Type II codes over IF_2r. In S. Boztas, & I. E. Shparlinski (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings (pp. 102-111). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2227). Springer-Verlag.

Type II codes over IF_2r. / Betsumiya, Koichi; Harada, Masaaki ; Munemasa, Akihiro.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings. ed. / Serdar Boztas; Igor E. Shparlinski. Springer-Verlag, 2001. p. 102-111 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2227).

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

Betsumiya, K, Harada, M & Munemasa, A 2001, Type II codes over IF_2r. in S Boztas & IE Shparlinski (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2227, Springer-Verlag, pp. 102-111, 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 2001, Melbourne, Australia, 01/11/26.

Betsumiya K, Harada M , Munemasa A. Type II codes over IF_2r. In Boztas S, Shparlinski IE, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings. Springer-Verlag. 2001. p. 102-111. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Betsumiya, Koichi ; Harada, Masaaki ; Munemasa, Akihiro. / Type II codes over IF_2r. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings. editor / Serdar Boztas ; Igor E. Shparlinski. Springer-Verlag, 2001. pp. 102-111 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{cc412349c6364cde96ef98ed45306667,

title = "Type II codes over IF2r",

abstract = "Motivated by the work of Pasquier and Wolfmann in 1980{\textquoteright}s, we define Type II codes over IF2r as self-dual codes with the property that their binary images with respect to a trace-orthogonal basis are doubly-even. We give a classification of Type II codes of length 8 over IF8, IF16 and IF32. We also characterize all Type II codes whose binary images are the extended Golay [24, 12, 8] code.",

author = "Koichi Betsumiya and Masaaki Harada and Akihiro Munemasa",

year = "2001",

month = jan,

day = "1",

language = "English",

isbn = "9783540456247",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "102--111",

editor = "Serdar Boztas and Shparlinski, {Igor E.}",

booktitle = "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings",

note = "14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 2001 ; Conference date: 26-11-2001 Through 30-11-2001",

}

TY - GEN

T1 - Type II codes over IF2r

AU - Betsumiya, Koichi

AU - Harada, Masaaki

AU - Munemasa, Akihiro

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Motivated by the work of Pasquier and Wolfmann in 1980’s, we define Type II codes over IF2r as self-dual codes with the property that their binary images with respect to a trace-orthogonal basis are doubly-even. We give a classification of Type II codes of length 8 over IF8, IF16 and IF32. We also characterize all Type II codes whose binary images are the extended Golay [24, 12, 8] code.

AB - Motivated by the work of Pasquier and Wolfmann in 1980’s, we define Type II codes over IF2r as self-dual codes with the property that their binary images with respect to a trace-orthogonal basis are doubly-even. We give a classification of Type II codes of length 8 over IF8, IF16 and IF32. We also characterize all Type II codes whose binary images are the extended Golay [24, 12, 8] code.

UR - http://www.scopus.com/inward/record.url?scp=84974659883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974659883&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84974659883

SN - 9783540456247

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 102

EP - 111

BT - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 14th International Symposium, AAECC-14, Proceedings

A2 - Boztas, Serdar

A2 - Shparlinski, Igor E.

PB - Springer-Verlag

T2 - 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 2001

Y2 - 26 November 2001 through 30 November 2001

ER -