Information on Result #737775

Linear OA(8170, 2097219, F8, 26) (dual of [2097219, 2097049, 27]-code), using construction X applied to Ce(25) ⊂ Ce(16) based on
  1. linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(815, 67, F8, 8) (dual of [67, 52, 9]-code), using
    • construction XX applied to C1 = C([62,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([62,6]) [i] based on
      1. linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
      2. linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(815, 63, F8, 8) (dual of [63, 48, 9]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      4. linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      5. linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code) (see above)

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 OOA(8170, 1048609, F8, 2, 26) (dual of [(1048609, 2), 2097048, 27]-NRT-code) [i]OOA Folding
2Linear OOA(8170, 699073, F8, 3, 26) (dual of [(699073, 3), 2097049, 27]-NRT-code) [i]