Binary optimal linear rate 1/2 codes

Koichi Betsumiya; T. Aaron Gulliver; Masaaki Harada

doi:10.1007/3-540-46796-3_44

Binary optimal linear rate 1/2 codes

Koichi Betsumiya, T. Aaron Gulliver, Masaaki Harada

INF - System Information Sciences

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

1 Citation (Scopus)

Abstract

In this paper, we classify the optimal linear [n, n/2] codes of length upto 12. We show that there is a unique optimal odd formally self-dual [20],[10],[6] code upto equivalence. We also show that at least one optimal linear [n, n/2] code is self-dual or formally self-dual for lengths upto 48 (except 38 and 40).

Original language	English
Title of host publication	Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings
Editors	Marc Fossorier, Shu Lin, Hideki Imai, Alain Poli
Publisher	Springer Verlag
Pages	462-471
Number of pages	10
ISBN (Print)	3540667237, 9783540667230
DOIs	https://doi.org/10.1007/3-540-46796-3_44
Publication status	Published - 1999
Event	13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1999 - Honolulu, United States Duration: 1999 Nov 15 → 1999 Nov 19

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1719
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1999
Country/Territory	United States
City	Honolulu
Period	99/11/15 → 99/11/19

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10.1007/3-540-46796-3_44

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Betsumiya, K., Gulliver, T. A., & Harada, M. (1999). Binary optimal linear rate 1/2 codes. In M. Fossorier, S. Lin, H. Imai, & A. Poli (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings (pp. 462-471). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1719). Springer Verlag. https://doi.org/10.1007/3-540-46796-3_44

Betsumiya, Koichi ; Gulliver, T. Aaron ; Harada, Masaaki. / Binary optimal linear rate 1/2 codes. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings. editor / Marc Fossorier ; Shu Lin ; Hideki Imai ; Alain Poli. Springer Verlag, 1999. pp. 462-471 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper, we classify the optimal linear [n, n/2] codes of length upto 12. We show that there is a unique optimal odd formally self-dual [20],[10],[6] code upto equivalence. We also show that at least one optimal linear [n, n/2] code is self-dual or formally self-dual for lengths upto 48 (except 38 and 40).",

author = "Koichi Betsumiya and Gulliver, {T. Aaron} and Masaaki Harada",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1999.; 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1999 ; Conference date: 15-11-1999 Through 19-11-1999",

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Betsumiya, K, Gulliver, TA & Harada, M 1999, Binary optimal linear rate 1/2 codes. in M Fossorier, S Lin, H Imai & A Poli (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1719, Springer Verlag, pp. 462-471, 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC 1999, Honolulu, United States, 99/11/15. https://doi.org/10.1007/3-540-46796-3_44

Binary optimal linear rate 1/2 codes. / Betsumiya, Koichi; Gulliver, T. Aaron; Harada, Masaaki.
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings. ed. / Marc Fossorier; Shu Lin; Hideki Imai; Alain Poli. Springer Verlag, 1999. p. 462-471 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1719).

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

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AB - In this paper, we classify the optimal linear [n, n/2] codes of length upto 12. We show that there is a unique optimal odd formally self-dual [20],[10],[6] code upto equivalence. We also show that at least one optimal linear [n, n/2] code is self-dual or formally self-dual for lengths upto 48 (except 38 and 40).

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

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Betsumiya K, Gulliver TA, Harada M. Binary optimal linear rate 1/2 codes. In Fossorier M, Lin S, Imai H, Poli A, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 13th International Symposium, AAECC-13, Proceedings. Springer Verlag. 1999. p. 462-471. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46796-3_44

Binary optimal linear rate 1/2 codes

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