Information on Result #1303651

Linear OA(1649, 131084, F16, 12) (dual of [131084, 131035, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1648, 131082, F16, 12) (dual of [131082, 131034, 13]-code), using
    • trace code [i] based on linear OA(25624, 65541, F256, 12) (dual of [65541, 65517, 13]-code), using
      • construction X applied to Ce(11) ⊂ Ce(9) [i] based on
        1. linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
        2. linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
        3. linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(1648, 131083, F16, 11) (dual of [131083, 131035, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 1648 > Vbs−1(k−1) = 237 921265 851072 487830 179622 045412 398819 429864 575482 003456 [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(1649, 131084, F16, 2, 12) (dual of [(131084, 2), 262119, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (37, 49, 131084)-net over F16 [i]
3Linear OOA(1649, 65542, F16, 2, 12) (dual of [(65542, 2), 131035, 13]-NRT-code) [i]OOA Folding