Information on Result #1302223

Linear OA(783, 235314, F7, 14) (dual of [235314, 235231, 15]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(782, 235312, F7, 14) (dual of [235312, 235230, 15]-code), using
    • trace code [i] based on linear OA(4941, 117656, F49, 14) (dual of [117656, 117615, 15]-code), using
      • construction X applied to Ce(13) ⊂ Ce(11) [i] based on
        1. linear OA(4940, 117649, F49, 14) (dual of [117649, 117609, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
        2. linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
        3. linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(782, 235313, F7, 13) (dual of [235313, 235231, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 782 > Vbs−1(k−1) = 130944 970006 701487 627698 900041 209833 571461 683915 612280 867995 164801 [i]
  3. linear OA(70, 1, F7, 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(783, 235314, F7, 2, 14) (dual of [(235314, 2), 470545, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(783, 235314, F7, 3, 14) (dual of [(235314, 3), 705859, 15]-NRT-code) [i]
3Digital (69, 83, 235314)-net over F7 [i]
4Linear OOA(783, 117657, F7, 2, 14) (dual of [(117657, 2), 235231, 15]-NRT-code) [i]OOA Folding