On the Classification of Self-dual -Codes

Cryptography and Coding - Lecture Notes in Computer Science ◽

10.1007/978-3-642-10868-6_6 ◽

2009 ◽

pp. 78-90 ◽

Cited By ~ 4

Author(s):

Masaaki Harada ◽

Akihiro Munemasa

Keyword(s):

Dual Codes

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On the classification of the extremal self-dual codes over small fields with 2-transitive automorphism groups

Designs Codes and Cryptography ◽

10.1007/s10623-012-9655-9 ◽

2012 ◽

Vol 70 (1-2) ◽

pp. 69-76 ◽

Cited By ~ 3

Author(s):

Anton Malevich ◽

Wolfgang Willems

Keyword(s):

Automorphism Groups ◽

Dual Codes ◽

Transitive Automorphism ◽

Small Fields

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Classification of extremal double circulant self-dual codes of lengths 74–88

Discrete Mathematics ◽

10.1016/j.disc.2006.05.004 ◽

2006 ◽

Vol 306 (17) ◽

pp. 2064-2072 ◽

Cited By ~ 12

Author(s):

T. Aaron Gulliver ◽

Masaaki Harada

Keyword(s):

Dual Codes

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Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2

Filomat ◽

10.2298/fil1405937k ◽

2014 ◽

Vol 28 (5) ◽

pp. 937-945 ◽

Cited By ~ 7

Author(s):

Suat Karadeniz ◽

Bahattin Yildiz ◽

Nuh Aydin

Keyword(s):

Dual Codes ◽

Weight Enumerators ◽

Extension Method ◽

Extremal Codes ◽

New Codes ◽

First Time

A classification of all four-circulant extremal codes of length 32 over F2 + uF2 is done by using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray images of these codes, a substantial number of extremal binary self-dual codes of length 64 are obtained. In particular a new code with ?=80 in W64,2 is found. Then applying an extension method from the literature to extremal self-dual codes of length 64, we have found many extremal binary self-dual codes of length 66. Among those, five of them are new codes in the sense that codes with these weight enumerators are constructed for the first time. These codes have the values ?=1, 30, 34, 84, 94 in W66,1.

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