Codes over \(\mathbb F_{3} + u\mathbb F_{3}\) and improvements to the bounds on ternary linear codes (Q1841528)

It is shown that a linear code with length \(n\) and Gray distance \(d\) over the ring \(\mathbb F_3 + u\mathbb F_3\) of order 9 can (using a Gray map) be mapped into a ternary linear code of length \(2n\), Hamming distance \(d\), and the same cardinality. A computer search for quasi-cyclic codes over \(\mathbb F_3 + u\mathbb F_3\) has been carried out; the results of this search lead to good (quasi-cyclic) ternary codes, six of which improve on the best known lower bound on the maximum possible minimum Hamming distance: \([208,8,127]\), \([150,10,85]\), \([160,10,91]\), \([170,10,97]\), \([180,10,103]\), \([190,10,110]\).