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Cyclic Self-DualZ4-Codes

✍ Scribed by Vera Pless; Patrick Solé; Zhongqiang Qian

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
306 KB
Volume
3
Category
Article
ISSN
1071-5797

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✦ Synopsis

For n odd, the Z 4 cyclic code generated by 2 is self-dual. We call this a trivial cyclic self-dual code. When do there exist nontrivial cyclic self-dual codes of odd length n? We give an answer in this paper by characterizing these n and describing generators of such codes; this yields an existence test for cyclic difference sets. We also give all examples of nontrivial cyclic self-dual codes up to length 39. From these nontrivial cyclic, self-dual codes, construction A yields unimodular lattices of Type I, some of which are extremal; extension and augmentation yields three new extremal Type II codes of length 32, and an extremal self-dual code of Type II of length 40.

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