Information on Result #675671

Linear OA(3168, 6593, F3, 30) (dual of [6593, 6425, 31]-code), using construction XX applied to Ce(30) ⊂ Ce(25) ⊂ Ce(24) based on
  1. linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(3137, 6561, F3, 26) (dual of [6561, 6424, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  3. linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(30, 1, F3, 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(3168, 3933, F3, 2, 30) (dual of [(3933, 2), 7698, 31]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3168, 3933, F3, 3, 30) (dual of [(3933, 3), 11631, 31]-NRT-code) [i]
3Linear OOA(3168, 3933, F3, 4, 30) (dual of [(3933, 4), 15564, 31]-NRT-code) [i]
4Linear OOA(3168, 3933, F3, 5, 30) (dual of [(3933, 5), 19497, 31]-NRT-code) [i]
5Digital (138, 168, 3933)-net over F3 [i]
6Linear OOA(3168, 3296, F3, 2, 30) (dual of [(3296, 2), 6424, 31]-NRT-code) [i]OOA Folding
7Linear OOA(3168, 1648, F3, 4, 30) (dual of [(1648, 4), 6424, 31]-NRT-code) [i]