Information on Result #684610

Linear OA(7101, 117678, F7, 19) (dual of [117678, 117577, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
  1. linear OA(797, 117650, F7, 19) (dual of [117650, 117553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  2. linear OA(773, 117650, F7, 15) (dual of [117650, 117577, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
  3. linear OA(74, 28, F7, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,7)), 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(7102, 117679, F7, 19) (dual of [117679, 117577, 20]-code) [i]Code Embedding in Larger Space
2Linear OA(7103, 117680, F7, 19) (dual of [117680, 117577, 20]-code) [i]
3Linear OOA(7101, 111923, F7, 2, 19) (dual of [(111923, 2), 223745, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(7101, 111923, F7, 3, 19) (dual of [(111923, 3), 335668, 20]-NRT-code) [i]
5Digital (82, 101, 111923)-net over F7 [i]
6Linear OA(7102, 117680, F7, 19) (dual of [117680, 117578, 20]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(7103, 117682, F7, 19) (dual of [117682, 117579, 20]-code) [i]
8Linear OOA(7101, 58839, F7, 2, 19) (dual of [(58839, 2), 117577, 20]-NRT-code) [i]OOA Folding
9Linear OOA(7101, 39226, F7, 3, 19) (dual of [(39226, 3), 117577, 20]-NRT-code) [i]
10Linear OOA(7101, 13075, F7, 19, 19) (dual of [(13075, 19), 248324, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row