Information on Result #686280

Linear OA(837, 2097168, F8, 6) (dual of [2097168, 2097131, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
  1. linear OA(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(822, 2097152, F8, 4) (dual of [2097152, 2097130, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
  4. linear OA(81, 16, F8, 1) (dual of [16, 15, 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 OA(838, 2097169, F8, 6) (dual of [2097169, 2097131, 7]-code) [i]Code Embedding in Larger Space
2Linear OOA(837, 2097168, F8, 2, 6) (dual of [(2097168, 2), 4194299, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(837, 2097168, F8, 3, 6) (dual of [(2097168, 3), 6291467, 7]-NRT-code) [i]
4Digital (31, 37, 2097168)-net over F8 [i]
5Linear OOA(837, 1048584, F8, 2, 6) (dual of [(1048584, 2), 2097131, 7]-NRT-code) [i]OOA Folding
6Linear OOA(837, 699056, F8, 3, 6) (dual of [(699056, 3), 2097131, 7]-NRT-code) [i]
7Linear OOA(837, 699056, F8, 6, 6) (dual of [(699056, 6), 4194299, 7]-NRT-code) [i]OA Folding and Stacking