Information on Result #735900

Linear OA(25667, 66313, F256, 24) (dual of [66313, 66246, 25]-code), using (u, u+v)-construction based on
  1. linear OA(25620, 775, F256, 12) (dual of [775, 755, 13]-code), using
    • construction XX applied to C1 = C([124,134]), C2 = C([123,133]), C3 = C1 + C2 = C([124,133]), and C∩ = C1 ∩ C2 = C([123,134]) [i] based on
      1. linear OA(25618, 771, F256, 11) (dual of [771, 753, 12]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {124,125,…,134}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(25618, 771, F256, 11) (dual of [771, 753, 12]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {123,124,…,133}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      3. linear OA(25620, 771, F256, 12) (dual of [771, 751, 13]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {123,124,…,134}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      4. linear OA(25616, 771, F256, 10) (dual of [771, 755, 11]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {124,125,…,133}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      5. linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
    • construction X applied to Ce(23) ⊂ Ce(22) [i] based on
      1. linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
      2. linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      3. linear OA(2560, 2, F256, 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(25667, 33156, F256, 2, 24) (dual of [(33156, 2), 66245, 25]-NRT-code) [i]OOA Folding
2Linear OOA(25667, 22104, F256, 3, 24) (dual of [(22104, 3), 66245, 25]-NRT-code) [i]
3Linear OOA(25667, 13262, F256, 5, 24) (dual of [(13262, 5), 66243, 25]-NRT-code) [i]