Information on Result #1303258

Linear OA(978, 531471, F9, 14) (dual of [531471, 531393, 15]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(977, 531469, F9, 14) (dual of [531469, 531392, 15]-code), using
    • construction X applied to Ce(13) ⊂ Ce(9) [i] based on
      1. linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      2. linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,9)), using
  2. linear OA(977, 531470, F9, 13) (dual of [531470, 531393, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 977 > Vbs−1(k−1) = 72849 307019 693718 783445 670310 328948 160147 005687 266098 586602 730314 719209 [i]
  3. linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), 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(978, 531471, F9, 2, 14) (dual of [(531471, 2), 1062864, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(978, 531471, F9, 3, 14) (dual of [(531471, 3), 1594335, 15]-NRT-code) [i]
3Digital (64, 78, 531471)-net over F9 [i]