Information on Result #731782

Linear OA(8128, 137, F8, 96) (dual of [137, 9, 97]-code), using juxtaposition based on
  1. linear OA(854, 63, F8, 44) (dual of [63, 9, 45]-code), using
    • the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
  2. linear OA(865, 74, F8, 51) (dual of [74, 9, 52]-code), using
    • construction XX applied to Ce(53) ⊂ Ce(45) ⊂ Ce(44) [i] based on
      1. linear OA(860, 64, F8, 54) (dual of [64, 4, 55]-code), using an extension Ce(53) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
      2. linear OA(856, 64, F8, 46) (dual of [64, 8, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
      3. linear OA(855, 64, F8, 45) (dual of [64, 9, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
      4. linear OA(84, 9, F8, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,8)), using
      5. linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using

Mode: Constructive and 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 OA(8128, 137, F8, 95) (dual of [137, 9, 96]-code) [i]Strength Reduction