Information on Result #675624

Linear OA(3242, 6596, F3, 44) (dual of [6596, 6354, 45]-code), using construction XX applied to Ce(43) ⊂ Ce(39) ⊂ Ce(37) based on
  1. linear OA(3233, 6561, F3, 44) (dual of [6561, 6328, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
  2. linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
  3. linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(3242, 4474, F3, 2, 44) (dual of [(4474, 2), 8706, 45]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3242, 4474, F3, 3, 44) (dual of [(4474, 3), 13180, 45]-NRT-code) [i]
3Linear OOA(3242, 4474, F3, 4, 44) (dual of [(4474, 4), 17654, 45]-NRT-code) [i]
4Linear OOA(3242, 4474, F3, 5, 44) (dual of [(4474, 5), 22128, 45]-NRT-code) [i]
5Digital (198, 242, 4474)-net over F3 [i]
6Linear OOA(3242, 3298, F3, 2, 44) (dual of [(3298, 2), 6354, 45]-NRT-code) [i]OOA Folding
7Linear OOA(3242, 1649, F3, 4, 44) (dual of [(1649, 4), 6354, 45]-NRT-code) [i]
8Linear OOA(3242, 1319, F3, 5, 44) (dual of [(1319, 5), 6353, 45]-NRT-code) [i]