Information on Result #684828

Linear OA(7103, 16839, F7, 23) (dual of [16839, 16736, 24]-code), using construction X applied to Ce(22) ⊂ Ce(16) based on
  1. linear OA(796, 16807, F7, 23) (dual of [16807, 16711, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(771, 16807, F7, 17) (dual of [16807, 16736, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(7104, 16840, F7, 23) (dual of [16840, 16736, 24]-code) [i]Code Embedding in Larger Space
2Linear OA(7105, 16841, F7, 23) (dual of [16841, 16736, 24]-code) [i]
3Linear OA(7106, 16842, F7, 23) (dual of [16842, 16736, 24]-code) [i]
4Linear OOA(7103, 16839, F7, 2, 23) (dual of [(16839, 2), 33575, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(7103, 16839, F7, 3, 23) (dual of [(16839, 3), 50414, 24]-NRT-code) [i]
6Digital (80, 103, 16839)-net over F7 [i]
7Linear OA(7104, 16841, F7, 23) (dual of [16841, 16737, 24]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(7105, 16843, F7, 23) (dual of [16843, 16738, 24]-code) [i]
9Linear OOA(7103, 8419, F7, 2, 23) (dual of [(8419, 2), 16735, 24]-NRT-code) [i]OOA Folding
10Linear OOA(7103, 5613, F7, 3, 23) (dual of [(5613, 3), 16736, 24]-NRT-code) [i]