Dual code: Difference between revisions

Revision as of 10:45, 18 December 2019

Revision as of 12:05, 11 March 2020

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

is a scalar product. In [[linear algebra]] terms, the dual code is the [[Annihilator (ring theory)|annihilator]] of ''C'' with respect to the [[bilinear form]] <,math>\langle\cdot\rangle</math>. 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>