Information on Result #676992

Linear OA(3136, 748, F3, 34) (dual of [748, 612, 35]-code), using construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(28) based on
  1. linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  2. linear OA(3118, 729, F3, 31) (dual of [729, 611, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  4. linear OA(34, 17, F3, 2) (dual of [17, 13, 3]-code), 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(3136, 631, F3, 2, 34) (dual of [(631, 2), 1126, 35]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3136, 631, F3, 3, 34) (dual of [(631, 3), 1757, 35]-NRT-code) [i]
3Linear OOA(3136, 631, F3, 4, 34) (dual of [(631, 4), 2388, 35]-NRT-code) [i]
4Linear OOA(3136, 631, F3, 5, 34) (dual of [(631, 5), 3019, 35]-NRT-code) [i]
5Digital (102, 136, 631)-net over F3 [i]