Information on Result #1299743

Linear OA(438, 16402, F4, 7) (dual of [16402, 16364, 8]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(437, 16400, F4, 7) (dual of [16400, 16363, 8]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
      4. linear OA(41, 16, F4, 1) (dual of [16, 15, 2]-code), using
  2. linear OA(437, 16401, F4, 6) (dual of [16401, 16364, 7]-code), using Gilbert–VarÅ¡amov bound and bm = 437 > Vbs−1(k−1) = 2401 173698 317620 887941 [i]
  3. linear OA(40, 1, F4, 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(438, 16402, F4, 2, 7) (dual of [(16402, 2), 32766, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(438, 16402, F4, 3, 7) (dual of [(16402, 3), 49168, 8]-NRT-code) [i]
3Digital (31, 38, 16402)-net over F4 [i]
4Linear OOA(438, 8201, F4, 2, 7) (dual of [(8201, 2), 16364, 8]-NRT-code) [i]OOA Folding