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SpiralSource (talk | contribs) Adding short description: "Array for a particular vector space" |
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{{Short description|Array for a particular vector space}}
In [[coding theory]], a '''standard array''' (or Slepian array) is a <math>q^{n-k}</math> by <math>q^{k}</math> array that lists all elements of a particular <math>\mathbb{F}_q^n</math> [[vector space]]. Standard arrays are used to [[Decoding methods|decode]] [[linear code]]s; i.e. to find the corresponding [[Code word (communication)|codeword]] for any received vector.
== Definition ==
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A standard array for an [''n'',''k'']-code is a <math>q^{n-k}</math> by <math>q^{k}</math> array where:
# The first row lists all [[Code word (communication)|codewords]] (with the <u>0</u> codeword on the extreme left)
# Each row is a [[coset]] with the [[coset leader]] in the first column
# The entry in the i-th row and j-th column is the sum of the i-th coset leader and the j-th codeword.
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