Information on Result #718424

Linear OA(992, 107, F9, 65) (dual of [107, 15, 66]-code), using construction XX applied to C1 = C([10,69]), C2 = C([1,59]), C3 = C1 + C2 = C([10,59]), and C∩ = C1 ∩ C2 = C([1,69]) based on
  1. linear OA(972, 80, F9, 60) (dual of [80, 8, 61]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,69}, and designed minimum distance d ≥ |I|+1 = 61 [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(965, 80, F9, 50) (dual of [80, 15, 51]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {10,11,…,59}, and designed minimum distance d ≥ |I|+1 = 51 [i]
  5. linear OA(910, 17, F9, 9) (dual of [17, 7, 10]-code), using
  6. linear OA(94, 10, F9, 4) (dual of [10, 6, 5]-code or 10-arc in PG(3,9)), 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.

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(992, 107, F9, 64) (dual of [107, 15, 65]-code) [i]Strength Reduction
2Linear OA(990, 105, F9, 63) (dual of [105, 15, 64]-code) [i]Truncation
3Linear OOA(992, 53, F9, 2, 65) (dual of [(53, 2), 14, 66]-NRT-code) [i]OOA Folding