Information on Result #1302191

Linear OA(777, 235316, F7, 13) (dual of [235316, 235239, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(776, 235314, F7, 13) (dual of [235314, 235238, 14]-code), using
    • trace code [i] based on linear OA(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-code), using
      • construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
        1. linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
        2. linear OA(4931, 117650, F49, 11) (dual of [117650, 117619, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
        3. linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(776, 235315, F7, 12) (dual of [235315, 235239, 13]-code), using Gilbert–VarÅ¡amov bound and bm = 776 > Vbs−1(k−1) = 1 113102 965470 602409 676983 885342 570968 825662 114260 117236 545713 [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(777, 235316, F7, 2, 13) (dual of [(235316, 2), 470555, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(777, 235316, F7, 3, 13) (dual of [(235316, 3), 705871, 14]-NRT-code) [i]
3Digital (64, 77, 235316)-net over F7 [i]
4Linear OOA(777, 117658, F7, 2, 13) (dual of [(117658, 2), 235239, 14]-NRT-code) [i]OOA Folding