Information on Result #684835

Linear OA(768, 16839, F7, 15) (dual of [16839, 16771, 16]-code), using construction X applied to Ce(14) ⊂ Ce(8) based on
  1. linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-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 OA(769, 16840, F7, 15) (dual of [16840, 16771, 16]-code) [i]Code Embedding in Larger Space
2Linear OA(770, 16841, F7, 15) (dual of [16841, 16771, 16]-code) [i]
3Linear OA(771, 16842, F7, 15) (dual of [16842, 16771, 16]-code) [i]
4Linear OA(767, 16838, F7, 14) (dual of [16838, 16771, 15]-code) [i]Truncation
5Linear OOA(768, 16839, F7, 2, 15) (dual of [(16839, 2), 33610, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(768, 16839, F7, 3, 15) (dual of [(16839, 3), 50449, 16]-NRT-code) [i]
7Digital (53, 68, 16839)-net over F7 [i]
8Linear OA(769, 16841, F7, 15) (dual of [16841, 16772, 16]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OOA(768, 8419, F7, 2, 15) (dual of [(8419, 2), 16770, 16]-NRT-code) [i]OOA Folding
10Linear OOA(768, 5613, F7, 3, 15) (dual of [(5613, 3), 16771, 16]-NRT-code) [i]
11Linear OOA(768, 2405, F7, 15, 15) (dual of [(2405, 15), 36007, 16]-NRT-code) [i]OOA Folding and Stacking with Additional Row