Information on Result #700071

Linear OA(12837, 16404, F128, 16) (dual of [16404, 16367, 17]-code), using construction X applied to Ce(15) ⊂ Ce(8) based on
  1. linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(12817, 16384, F128, 9) (dual of [16384, 16367, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(1286, 20, F128, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), 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
1OA(6444, 16404, S64, 16) [i]Discarding Parts of the Base for OAs
2Linear OOA(12837, 12473, F128, 2, 16) (dual of [(12473, 2), 24909, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12837, 12473, F128, 3, 16) (dual of [(12473, 3), 37382, 17]-NRT-code) [i]
4Linear OOA(12837, 12473, F128, 4, 16) (dual of [(12473, 4), 49855, 17]-NRT-code) [i]
5Digital (21, 37, 12473)-net over F128 [i]
6Linear OOA(12837, 8202, F128, 2, 16) (dual of [(8202, 2), 16367, 17]-NRT-code) [i]OOA Folding
7Linear OOA(12837, 5468, F128, 3, 16) (dual of [(5468, 3), 16367, 17]-NRT-code) [i]
8Linear OOA(12837, 4101, F128, 4, 16) (dual of [(4101, 4), 16367, 17]-NRT-code) [i]