Information on Result #1303655

Linear OA(1651, 131090, F16, 12) (dual of [131090, 131039, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(1650, 131088, F16, 12) (dual of [131088, 131038, 13]-code), using
    • trace code [i] based on linear OA(25625, 65544, F256, 12) (dual of [65544, 65519, 13]-code), using
      • construction X applied to Ce(11) ⊂ Ce(8) [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(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
        3. linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
  2. linear OA(1650, 131089, F16, 11) (dual of [131089, 131039, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 1650 > Vbs−1(k−1) = 238 030195 374032 030705 784269 317830 412494 336250 444404 605371 [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(1651, 131090, F16, 2, 12) (dual of [(131090, 2), 262129, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (39, 51, 131090)-net over F16 [i]
3Linear OOA(1651, 65545, F16, 2, 12) (dual of [(65545, 2), 131039, 13]-NRT-code) [i]OOA Folding