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Lowest density MDS codes over extension alphabets

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2 Author(s)
Louidor, E. ; Dept. of Math., British Columbia Univ., Vancouver, BC, Canada ; Roth, R.M.

Let F be a finite field and b be a positive integer. A construction is presented of codes over the alphabet Fb with the following three properties: i) the codes are maximum-distance separable (MDS) over Fb, ii) they are linear over F, and iii) they have systematic generator and parity-check matrices over F with the smallest possible number of nonzero entries. Furthermore, for the case F=GF(2), the construction is the longest possible among all codes that satisfy properties i)-iii).

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Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 7 )