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Bounds on the minimum support weights

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4 Author(s)
Helleseth, T. ; Dept. of Inf., Bergen Univ., Norway ; Klove, T. ; Levenshtein, V.I. ; Ytrehus, O.

The minimum support weight, dr(C), of a linear code C over GF(q) is the minimal size of the support of an r-dimensional subcode of C. A number of bounds on dr(C) are derived, generalizing the Plotkin bound and the Griesmer bound, as well as giving two new existential bounds. As the main result, it is shown that there exist codes of any given rate R whose ratio dr/d1 is lower bounded by a number ranging from (qr-1)/(qr -qr-1) to r, depending on R

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 2 )