Dual code: Difference between revisions

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==Self-dual codes==

A '''self-dual code''' is one which is its own dual. This implies that ''n'' is even and dim ''C'' = ''n''/2. Self-dual codes can be classified into four types<ref>{{cite book | last=Conway | first=J.H. | authorlink=John Conway | coauthors=Sloane,N.J.A. | authorlink2=Neil Sloane | title=Sphere packings, lattices and groups | series=Grundlehren der mathematischen Wissenschaften | volume=290 | publisher=[[Springer-Verlag]] | date=1988 | isbn=0-387-96617-X | pagespage=77}}</ref>:

*'''Type I''' codes are binary self-dual codes which are not [[doubly-even code|doubly-even]]. Type I codes are always [[even code|even]] (every codeword has even [[Hamming weight]]).

*'''Type II''' codes are binary self-dual codes which are doubly-even.

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{{reflist}}

{{refbegin}}

* {{cite book | last=Hill | first=Raymond | title=A first course in coding theory | publisher=[[Oxford University Press]] | series=Oxford Applied Mathematics and Computing Science Series | date=1986 | isbn=0-19-853803-0 | pagespage=67 }}

* {{cite book | last = Pless | first = Vera | authorlink=Vera Pless | title = Introduction to the theory of error-correcting codes | publisher = [[John Wiley & Sons]]|series = Wiley-Interscience Series in Discrete Mathematics | date = 1982| isbn = 0-471-08684-3 | pagespage=8 }}

* {{cite book | author=J.H. van Lint | title=Introduction to Coding Theory | edition=2nd ed | publisher=Springer-Verlag | series=[[Graduate Texts in Mathematics|GTM]] | volume=86 | date=1992 | isbn=3-540-54894-7 | pagespage=34}}

{{refend}}