Information on Result #718419

Linear OA(997, 112, F9, 69) (dual of [112, 15, 70]-code), using construction XX applied to C1 = C([11,69]), C2 = C([1,59]), C3 = C1 + C2 = C([11,59]), and C∩ = C1 ∩ C2 = C([1,69]) based on
  1. linear OA(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,69}, and designed minimum distance d ≥ |I|+1 = 60 [i]
  2. linear OA(971, 80, F9, 59) (dual of [80, 9, 60]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,59], and designed minimum distance d ≥ |I|+1 = 60 [i]
  3. linear OA(976, 80, F9, 69) (dual of [80, 4, 70]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,69], and designed minimum distance d ≥ |I|+1 = 70 [i]
  4. linear OA(964, 80, F9, 49) (dual of [80, 16, 50]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {11,12,…,59}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  5. linear OA(910, 16, F9, 9) (dual of [16, 6, 10]-code), using
  6. linear OA(910, 16, F9, 9) (dual of [16, 6, 10]-code) (see above)

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(996, 111, F9, 68) (dual of [111, 15, 69]-code) [i]Truncation
2Linear OA(995, 110, F9, 67) (dual of [110, 15, 68]-code) [i]
3Linear OA(993, 108, F9, 65) (dual of [108, 15, 66]-code) [i]
4Linear OOA(997, 56, F9, 2, 69) (dual of [(56, 2), 15, 70]-NRT-code) [i]OOA Folding