Information on Result #691643

Linear OA(16100, 1048600, F16, 21) (dual of [1048600, 1048500, 22]-code), using construction X applied to Ce(20) ⊂ Ce(16) based on
  1. linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), 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(16101, 1048601, F16, 21) (dual of [1048601, 1048500, 22]-code) [i]Code Embedding in Larger Space
2Linear OOA(16100, 993617, F16, 2, 21) (dual of [(993617, 2), 1987134, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Digital (79, 100, 993617)-net over F16 [i]
4Linear OA(16101, 1048602, F16, 21) (dual of [1048602, 1048501, 22]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OA(16102, 1048604, F16, 21) (dual of [1048604, 1048502, 22]-code) [i]
6Linear OOA(16100, 524300, F16, 2, 21) (dual of [(524300, 2), 1048500, 22]-NRT-code) [i]OOA Folding