It is proved that ternary codes with parameters [15,8,6], [15,9,5], [16,6,8], and [16,7,7] do not exist. This result solves the problem of finding optimal ternary linear codes of length at most 21. A table is given, showing the exact value of d/sub 3/(n,k) for n/spl les/21 with the earliest references.>

It is proved that ternary codes with parameters [40,5,25] and [148,5,98] do not exist. A new ternary code is constructed with parameters [47.5,30]. The results solve the problem of finding the smallest n for which a ternary [n, 5, d] code exists for d=25; 29, 30, and 98. Several new ternary linear codes of dimension 6 are found, including one two-weight code giving rise to a new strongly regular graph.

Optimal ternary linear codes with parameters /spl lsqb/29,5,18/spl rsqb/, /spl lsqb/34,5,21/spl rsqb/, /spl lsqb/43,5,27/spl rsqb/, /spl lsqb/61,5,39/spl rsqb/, and /spl lsqb/31,6,18/spl rsqb/ have been found. Codes with these parameters were not known until now.>

There are many ways to find lower bounds for the minimum distance of a cyclic code, based on investigation of the defining set. Some new theorems are derived. These and earlier techniques are applied to find lower bounds for the minimum distance of ternary cyclic codes. Furthermore, the exact minimum distance of ternary cyclic codes of length less than 40 is computed numerically. A table is given containing all ternary cyclic codes of length less than 40 and having a minimum distance exceeding the BCH bound. It seems that almost all lower bounds are equal to the minimum distance. Especially shifting, which is also done by computer, seems to be very powerful. For length 40>