Dual code: Difference between revisions

Revision as of 11:02, 11 July 2008

Revision as of 12:23, 11 July 2008

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where

:<math>\langle x, c \rangle = \sum_{i=1}^n x_i {c_i}^p </math>

and ''p'' is thescalar [[characteristicproduct. (algebra)|characteristic]] of '''F'''_''q''. In [[linear algebra]] terms, the dual code is the [[annihilator]] of ''C'' with respect to the [[bilinear form]] <,>. The [[Dimension_(vector_space)|dimension]] of ''C'' and its dual always add up to the length ''n'':

:<math>\dim C + \dim C^\perp = n.</math>

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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 | pages=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 | pages=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 | pages=34}}

{{refend}}