Information on Result #684879

Linear OA(746, 16828, F7, 10) (dual of [16828, 16782, 11]-code), using construction XX applied to Ce(9) ⊂ Ce(5) ⊂ Ce(4) based on
  1. linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  2. linear OA(726, 16807, F7, 6) (dual of [16807, 16781, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(721, 16807, F7, 5) (dual of [16807, 16786, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  4. linear OA(74, 20, F7, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,7)), using
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using

Mode: Constructive and 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(746, 16828, F7, 2, 10) (dual of [(16828, 2), 33610, 11]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(746, 16828, F7, 3, 10) (dual of [(16828, 3), 50438, 11]-NRT-code) [i]
3Digital (36, 46, 16828)-net over F7 [i]
4Linear OOA(746, 8414, F7, 2, 10) (dual of [(8414, 2), 16782, 11]-NRT-code) [i]OOA Folding
5Linear OOA(746, 5609, F7, 3, 10) (dual of [(5609, 3), 16781, 11]-NRT-code) [i]