Information on Result #733373

Linear OA(27104, 531553, F27, 22) (dual of [531553, 531449, 23]-code), using (u, u+v)-construction based on
  1. linear OA(2719, 108, F27, 11) (dual of [108, 89, 12]-code), using
    • construction XX applied to C1 = C([103,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([103,9]) [i] based on
      1. linear OA(2717, 104, F27, 10) (dual of [104, 87, 11]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(2717, 104, F27, 10) (dual of [104, 87, 11]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(2719, 104, F27, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      4. linear OA(2715, 104, F27, 9) (dual of [104, 89, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(2785, 531445, F27, 22) (dual of [531445, 531360, 23]-code), using
    • construction X applied to Ce(21) ⊂ Ce(20) [i] based on
      1. linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
      2. linear OA(2781, 531441, F27, 21) (dual of [531441, 531360, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      3. linear OA(270, 4, F27, 0) (dual of [4, 4, 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 OOA(27104, 265776, F27, 2, 22) (dual of [(265776, 2), 531448, 23]-NRT-code) [i]OOA Folding
2Linear OOA(27104, 48323, F27, 22, 22) (dual of [(48323, 22), 1063002, 23]-NRT-code) [i]OA Folding and Stacking