BOUNDS ON THE MINIMUM SUPPORT WEIGHTS

The minimum support weight, d(r)(C), of a linear code C over GF(q) is the minimal size of the support of an r-dimensional subcode of C. A nu mber of bounds on d(r)(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 ra te R whose ratio d(r)/d(1) is lower bounded by a number ranging from ( q(r) - 1)/(q(r) - q(r-1)) to r, depending on R.