Information on Result #675704

Linear OA(3114, 6596, F3, 20) (dual of [6596, 6482, 21]-code), using construction XX applied to Ce(19) ⊂ Ce(15) ⊂ Ce(13) based on
  1. linear OA(3105, 6561, F3, 20) (dual of [6561, 6456, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(381, 6561, F3, 16) (dual of [6561, 6480, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  3. linear OA(373, 6561, F3, 14) (dual of [6561, 6488, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  4. linear OA(36, 32, F3, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,3)), using
  5. linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-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(3114, 3719, F3, 2, 20) (dual of [(3719, 2), 7324, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3114, 3719, F3, 3, 20) (dual of [(3719, 3), 11043, 21]-NRT-code) [i]
3Linear OOA(3114, 3719, F3, 4, 20) (dual of [(3719, 4), 14762, 21]-NRT-code) [i]
4Linear OOA(3114, 3719, F3, 5, 20) (dual of [(3719, 5), 18481, 21]-NRT-code) [i]
5Digital (94, 114, 3719)-net over F3 [i]
6Linear OOA(3114, 3298, F3, 2, 20) (dual of [(3298, 2), 6482, 21]-NRT-code) [i]OOA Folding
7Linear OOA(3114, 1649, F3, 4, 20) (dual of [(1649, 4), 6482, 21]-NRT-code) [i]
8Linear OOA(3114, 1319, F3, 5, 20) (dual of [(1319, 5), 6481, 21]-NRT-code) [i]