Information on Result #675641

Linear OA(3216, 6593, F3, 39) (dual of [6593, 6377, 40]-code), using construction XX applied to Ce(39) ⊂ Ce(34) ⊂ Ce(33) based on
  1. 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]
  2. linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  3. linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(3216, 4303, F3, 2, 39) (dual of [(4303, 2), 8390, 40]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3216, 4303, F3, 3, 39) (dual of [(4303, 3), 12693, 40]-NRT-code) [i]
3Linear OOA(3216, 4303, F3, 4, 39) (dual of [(4303, 4), 16996, 40]-NRT-code) [i]
4Linear OOA(3216, 4303, F3, 5, 39) (dual of [(4303, 5), 21299, 40]-NRT-code) [i]
5Digital (177, 216, 4303)-net over F3 [i]
6Linear OOA(3216, 3296, F3, 2, 39) (dual of [(3296, 2), 6376, 40]-NRT-code) [i]OOA Folding
7Linear OOA(3216, 1648, F3, 4, 39) (dual of [(1648, 4), 6376, 40]-NRT-code) [i]