Information on Result #686388

Linear OA(8108, 2097162, F8, 18) (dual of [2097162, 2097054, 19]-code), using construction XX applied to Ce(17) ⊂ Ce(16) ⊂ Ce(14) based on
  1. linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  4. linear OA(80, 8, F8, 0) (dual of [8, 8, 1]-code), using
  5. linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-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(8108, 1063778, F8, 2, 18) (dual of [(1063778, 2), 2127448, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8108, 1063778, F8, 3, 18) (dual of [(1063778, 3), 3191226, 19]-NRT-code) [i]
3Digital (90, 108, 1063778)-net over F8 [i]
4Linear OOA(8108, 1048581, F8, 2, 18) (dual of [(1048581, 2), 2097054, 19]-NRT-code) [i]OOA Folding
5Linear OOA(8108, 699054, F8, 3, 18) (dual of [(699054, 3), 2097054, 19]-NRT-code) [i]
6Linear OOA(8108, 233018, F8, 18, 18) (dual of [(233018, 18), 4194216, 19]-NRT-code) [i]OA Folding and Stacking