Information on Result #1298654

Linear OA(3143, 531488, F3, 17) (dual of [531488, 531345, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3139, 531483, F3, 17) (dual of [531483, 531344, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(12) [i] based on
      1. linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. 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]
      3. linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
  2. linear OA(3139, 531484, F3, 13) (dual of [531484, 531345, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 3139 > Vbs−1(k−1) = 4343 566634 555197 448404 592507 995307 586702 236388 620270 020217 835451 [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(3143, 265744, F3, 2, 17) (dual of [(265744, 2), 531345, 18]-NRT-code) [i]OOA Folding
2Linear OOA(3143, 132872, F3, 4, 17) (dual of [(132872, 4), 531345, 18]-NRT-code) [i]