Information on Result #691661

Linear OA(16107, 1048607, F16, 22) (dual of [1048607, 1048500, 23]-code), using construction X applied to Ce(21) ⊂ Ce(16) based on
  1. linear OA(16101, 1048576, F16, 22) (dual of [1048576, 1048475, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(166, 31, F16, 4) (dual of [31, 25, 5]-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(16108, 1048608, F16, 22) (dual of [1048608, 1048500, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(16109, 1048609, F16, 22) (dual of [1048609, 1048500, 23]-code) [i]
3Linear OOA(16107, 1048607, F16, 2, 22) (dual of [(1048607, 2), 2097107, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Digital (85, 107, 1048607)-net over F16 [i]
5Linear OA(16108, 1048609, F16, 22) (dual of [1048609, 1048501, 23]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(16109, 1048611, F16, 22) (dual of [1048611, 1048502, 23]-code) [i]
7Linear OOA(16107, 524303, F16, 2, 22) (dual of [(524303, 2), 1048499, 23]-NRT-code) [i]OOA Folding