Information on Result #1298323

Linear OA(3102, 531473, F3, 12) (dual of [531473, 531371, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(398, 531467, F3, 12) (dual of [531467, 531369, 13]-code), using
    • construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
      1. linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
      4. linear OA(31, 26, F3, 1) (dual of [26, 25, 2]-code), using
  2. linear OA(398, 531469, F3, 9) (dual of [531469, 531371, 10]-code), using Gilbert–VarÅ¡amov bound and bm = 398 > Vbs−1(k−1) = 40 412600 174106 948585 131762 490626 303838 690289 [i]
  3. linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), 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(3102, 265736, F3, 2, 12) (dual of [(265736, 2), 531370, 13]-NRT-code) [i]OOA Folding
2Linear OOA(3102, 132868, F3, 4, 12) (dual of [(132868, 4), 531370, 13]-NRT-code) [i]