Standard Array
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In coding theory, a standard array (or Slepian array) is a qn k by qk array that lists all elements of a particular mathbb{F}_q^n vector space. Standard arrays are used to decode linear codes; i.e. to find the corresponding codeword for any received vector. Note that the above is only one possibility for the standard array; had 00011 been chosen as the first coset leader of weight two, another standard array representing the code would have been constructed. Note that...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In coding theory, a standard array (or Slepian array) is a qn k by qk array that lists all elements of a particular mathbb{F}_q^n vector space. Standard arrays are used to decode linear codes; i.e. to find the corresponding codeword for any received vector. Note that the above is only one possibility for the standard array; had 00011 been chosen as the first coset leader of weight two, another standard array representing the code would have been constructed. Note that the first row contains the 0 vector and the codewords of C3 (0 itself being a codeword). Also, the leftmost column contains the vectors of minimum weight enumerating vectors of weight 1 first and then using vectors of weight 2. Note also that each possible vector in the vector space appears exactly once.
