Information on Result #1302832

Linear OA(8128, 2097196, F8, 20) (dual of [2097196, 2097068, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(8127, 2097194, F8, 20) (dual of [2097194, 2097067, 21]-code), using
    • construction X applied to Ce(19) ⊂ Ce(13) [i] based on
      1. linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
      2. linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
  2. linear OA(8127, 2097195, F8, 19) (dual of [2097195, 2097068, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 8127 > Vbs−1(k−1) = 156634 514891 273957 503802 387268 063775 593707 471630 844215 705938 065895 684753 181573 327013 377299 903284 470260 788666 155224 [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(8128, 2097196, F8, 2, 20) (dual of [(2097196, 2), 4194264, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8128, 2097196, F8, 3, 20) (dual of [(2097196, 3), 6291460, 21]-NRT-code) [i]
3Digital (108, 128, 2097196)-net over F8 [i]
4Linear OOA(8128, 1048598, F8, 2, 20) (dual of [(1048598, 2), 2097068, 21]-NRT-code) [i]OOA Folding