Information on Result #1302607

Linear OA(883, 524304, F8, 14) (dual of [524304, 524221, 15]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(882, 524302, F8, 14) (dual of [524302, 524220, 15]-code), using
    • trace code [i] based on linear OA(6441, 262151, F64, 14) (dual of [262151, 262110, 15]-code), using
      • construction X applied to Ce(13) ⊂ Ce(11) [i] based on
        1. linear OA(6440, 262144, F64, 14) (dual of [262144, 262104, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
        2. linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
        3. linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(882, 524303, F8, 13) (dual of [524303, 524221, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 882 > Vbs−1(k−1) = 12467 071163 921913 335205 861863 299549 766260 685392 859729 835010 695915 934989 [i]
  3. linear OA(80, 1, F8, 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(883, 524304, F8, 2, 14) (dual of [(524304, 2), 1048525, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(883, 524304, F8, 3, 14) (dual of [(524304, 3), 1572829, 15]-NRT-code) [i]
3Digital (69, 83, 524304)-net over F8 [i]
4Linear OOA(883, 262152, F8, 2, 14) (dual of [(262152, 2), 524221, 15]-NRT-code) [i]OOA Folding