Information on Result #675705

Linear OA(3113, 6594, F3, 20) (dual of [6594, 6481, 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, 31, F3, 3) (dual of [31, 25, 4]-code or 31-cap in PG(5,3)), using
  5. linear OA(31, 2, F3, 1) (dual of [2, 1, 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(3113, 3498, F3, 2, 20) (dual of [(3498, 2), 6883, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3113, 3498, F3, 3, 20) (dual of [(3498, 3), 10381, 21]-NRT-code) [i]
3Linear OOA(3113, 3498, F3, 4, 20) (dual of [(3498, 4), 13879, 21]-NRT-code) [i]
4Linear OOA(3113, 3498, F3, 5, 20) (dual of [(3498, 5), 17377, 21]-NRT-code) [i]
5Digital (93, 113, 3498)-net over F3 [i]
6Linear OOA(3113, 3297, F3, 2, 20) (dual of [(3297, 2), 6481, 21]-NRT-code) [i]OOA Folding
7Linear OOA(3113, 2198, F3, 3, 20) (dual of [(2198, 3), 6481, 21]-NRT-code) [i]