Information on Result #1299077

Linear OA(3194, 19734, F3, 30) (dual of [19734, 19540, 31]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3190, 19729, F3, 30) (dual of [19729, 19539, 31]-code), using
    • construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
      1. linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
      2. linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      3. linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
  2. linear OA(3190, 19730, F3, 26) (dual of [19730, 19540, 27]-code), using Gilbert–VarÅ¡amov bound and bm = 3190 > Vbs−1(k−1) = 508627 661796 457718 619503 644009 004568 375613 265565 614716 428013 791725 002707 362040 167446 458819 [i]
  3. linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(3194, 9867, F3, 2, 30) (dual of [(9867, 2), 19540, 31]-NRT-code) [i]OOA Folding
2Linear OOA(3194, 6578, F3, 3, 30) (dual of [(6578, 3), 19540, 31]-NRT-code) [i]