Information on Result #722195

Linear OA(16109, 278, F16, 59) (dual of [278, 169, 60]-code), using construction XX applied to C1 = C([250,50]), C2 = C([1,53]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([250,53]) based on
  1. linear OA(1697, 255, F16, 56) (dual of [255, 158, 57]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−5,−4,…,50}, and designed minimum distance d ≥ |I|+1 = 57 [i]
  2. linear OA(1691, 255, F16, 53) (dual of [255, 164, 54]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
  3. linear OA(16102, 255, F16, 59) (dual of [255, 153, 60]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−5,−4,…,53}, and designed minimum distance d ≥ |I|+1 = 60 [i]
  4. linear OA(1686, 255, F16, 50) (dual of [255, 169, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
  5. linear OA(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
  6. linear OA(162, 7, F16, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,16)), 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 OA(16108, 277, F16, 58) (dual of [277, 169, 59]-code) [i]Truncation
2Linear OOA(16109, 139, F16, 2, 59) (dual of [(139, 2), 169, 60]-NRT-code) [i]OOA Folding