Information on Result #1301345

Linear OA(554, 78151, F5, 9) (dual of [78151, 78097, 10]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(553, 78149, F5, 9) (dual of [78149, 78096, 10]-code), using
    • construction X applied to Ce(8) ⊂ Ce(5) [i] based on
      1. linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
        • the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
  2. linear OA(553, 78150, F5, 8) (dual of [78150, 78097, 9]-code), using Gilbert–VarÅ¡amov bound and bm = 553 > Vbs−1(k−1) = 57855 732842 240392 377082 162564 064053 [i]
  3. linear OA(50, 1, F5, 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(554, 78151, F5, 2, 9) (dual of [(78151, 2), 156248, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(554, 78151, F5, 3, 9) (dual of [(78151, 3), 234399, 10]-NRT-code) [i]
3Digital (45, 54, 78151)-net over F5 [i]