Information on Result #1303631

Linear OA(1633, 131084, F16, 8) (dual of [131084, 131051, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1632, 131082, F16, 8) (dual of [131082, 131050, 9]-code), using
    • trace code [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
      • construction X applied to Ce(7) ⊂ Ce(5) [i] based on
        1. linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(1632, 131083, F16, 7) (dual of [131083, 131051, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 1632 > Vbs−1(k−1) = 80246 304169 023850 471583 378724 815956 [i]
  3. linear OA(160, 1, F16, 0) (dual of [1, 1, 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(1633, 131084, F16, 2, 8) (dual of [(131084, 2), 262135, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (25, 33, 131084)-net over F16 [i]
3Linear OOA(1633, 65542, F16, 2, 8) (dual of [(65542, 2), 131051, 9]-NRT-code) [i]OOA Folding