On optimal non-projective ternary linear codes

We prove the existence of a [406,6,270]3[406,6,270]3 code and the nonexistence of linear codes with parameters [458,6,304]3[458,6,304]3, [467,6,310]3[467,6,310]3, [471,6,313]3[471,6,313]3, [522,6,347]3[522,6,347]3. These yield that n3(6,d)=g3(6,d)n3(6,d)=g3(6,d) for 268⩽d⩽270268⩽d⩽270, n3(6,d)=g3(6,d)+1n3(6,d)=g3(6,d)+1 for d∈{280-282,304-306,313-315,347,348},d∈{280-282,304-306,313-315,347,348},n3(6,d)=g3(6,d)n3(6,d)=g3(6,d) or g3(6,d)+1g3(6,d)+1 for 298⩽d⩽301298⩽d⩽301 and n3(6,d)=g3(6,d)+1n3(6,d)=g3(6,d)+1 or g3(6,d)+2g3(6,d)+2 for 310⩽d⩽312310⩽d⩽312, where nq(k,d)nq(k,d) denotes the minimum length n   for which an [n,k,d]q[n,k,d]q code exists and gq(k,d)=∑i=0k-1⌈d/qi⌉.