Information on Result #699684

Linear OA(12862, 2097184, F128, 19) (dual of [2097184, 2097122, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,5]) based on
  1. linear OA(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(1287, 31, F128, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,128)), 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(3287, 2097184, S32, 19) [i]Discarding Parts of the Base for OAs
2Linear OOA(12862, 2057335, F128, 2, 19) (dual of [(2057335, 2), 4114608, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12862, 2057335, F128, 3, 19) (dual of [(2057335, 3), 6171943, 20]-NRT-code) [i]
4Linear OOA(12862, 2057335, F128, 4, 19) (dual of [(2057335, 4), 8229278, 20]-NRT-code) [i]
5Digital (43, 62, 2057335)-net over F128 [i]
6Linear OOA(12862, 1048592, F128, 2, 19) (dual of [(1048592, 2), 2097122, 20]-NRT-code) [i]OOA Folding
7Linear OOA(12862, 699061, F128, 3, 19) (dual of [(699061, 3), 2097121, 20]-NRT-code) [i]
8Linear OOA(12862, 524296, F128, 4, 19) (dual of [(524296, 4), 2097122, 20]-NRT-code) [i]
9Linear OOA(12862, 233020, F128, 19, 19) (dual of [(233020, 19), 4427318, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row