The MDS Conjecture
نویسنده
چکیده
De nition. The reason for the title MDS is because of the tie with maximum distance separable codes. Indeed, a [n; k; d] linear code C is said to be maximum distance separable if it meets the Singleton Bound k n d + 1 at equality. This bound is simply proved by noting that in a code of distance d, any choice of n d+ 1 entries can determine at most one codeword of C, so in the case of equality, any choice must yield some codeword.
منابع مشابه
MDS matrices over small fields: A proof of the GM-MDS conjecture
The GM-MDS conjecture of Dau et al. (ISIT 2014) speculates that the MDS condition, which guarantees the existence of MDS matrices with a prescribed set of zeros over large fields, is in fact sufficient for existence of such matrices over small fields. We prove this conjecture.
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