Information on Result #684698

Linear OA(772, 117679, F7, 13) (dual of [117679, 117607, 14]-code), using construction XX applied to Ce(12) ⊂ Ce(8) ⊂ Ce(7) based on
  1. linear OA(767, 117649, F7, 13) (dual of [117649, 117582, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  4. linear OA(74, 29, F7, 3) (dual of [29, 25, 4]-code or 29-cap in PG(3,7)), using
  5. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), 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(772, 117679, F7, 2, 13) (dual of [(117679, 2), 235286, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(772, 117679, F7, 3, 13) (dual of [(117679, 3), 352965, 14]-NRT-code) [i]
3Digital (59, 72, 117679)-net over F7 [i]
4Linear OOA(772, 58839, F7, 2, 13) (dual of [(58839, 2), 117606, 14]-NRT-code) [i]OOA Folding
5Linear OOA(772, 39226, F7, 3, 13) (dual of [(39226, 3), 117606, 14]-NRT-code) [i]
6Linear OOA(772, 19613, F7, 13, 13) (dual of [(19613, 13), 254897, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row