Information on Result #699687

Linear OA(12870, 2097192, F128, 21) (dual of [2097192, 2097122, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,5]) based on
  1. linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
  3. linear OA(1289, 39, F128, 9) (dual of [39, 30, 10]-code or 39-arc in PG(8,128)), 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
1Linear OOA(12870, 2097192, F128, 2, 21) (dual of [(2097192, 2), 4194314, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12870, 2097192, F128, 3, 21) (dual of [(2097192, 3), 6291506, 22]-NRT-code) [i]
3Linear OOA(12870, 2097192, F128, 4, 21) (dual of [(2097192, 4), 8388698, 22]-NRT-code) [i]
4Digital (49, 70, 2097192)-net over F128 [i]
5Linear OOA(12870, 1048596, F128, 2, 21) (dual of [(1048596, 2), 2097122, 22]-NRT-code) [i]OOA Folding
6Linear OOA(12870, 699064, F128, 3, 21) (dual of [(699064, 3), 2097122, 22]-NRT-code) [i]
7Linear OOA(12870, 524298, F128, 4, 21) (dual of [(524298, 4), 2097122, 22]-NRT-code) [i]
8Linear OOA(12870, 209719, F128, 21, 21) (dual of [(209719, 21), 4404029, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row