Block code: Difference between revisions

Revision as of 04:11, 8 January 2025

Revision as of 18:23, 8 January 2025

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=== The alphabet Σ ===

The data stream to be encoded is modeled as a [[string (computer science)|string]] over some '''alphabet''' <math>\Sigma</math>. The size <math>|\Sigma|</math> of the alphabet is often written as <math>q</math>. If <math>q=2</math>, then the block code is called a ''binary'' block code. In many applications it is useful to consider <math>q</math> to be a [[prime power]], and to identify <math>\Sigma</math> with the [[finite field]] <math>\mathbb F_q</math>.

, and to identify <math>\Sigma</math> with the [[finite field]] <math>\mathbb F_q</math>.

=== The message length ''k'' ===