Information on Result #1303773

Linear OA(16109, 1048611, F16, 22) (dual of [1048611, 1048502, 23]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(16107, 1048607, F16, 22) (dual of [1048607, 1048500, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(16) [i] 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
  2. linear OA(16107, 1048609, F16, 21) (dual of [1048609, 1048502, 22]-code), using Gilbert–VarÅ¡amov bound and bm = 16107 > Vbs−1(k−1) = 353090 277226 406078 116575 286121 936373 062540 042872 065185 035191 613776 459335 310062 216331 505724 226055 090467 480985 355830 227884 218171 [i]
  3. linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using

Mode: 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(16109, 1048611, F16, 2, 22) (dual of [(1048611, 2), 2097113, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (87, 109, 1048611)-net over F16 [i]
3Linear OOA(16109, 524305, F16, 2, 22) (dual of [(524305, 2), 1048501, 23]-NRT-code) [i]OOA Folding