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…mehr

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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 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.