Information on Result #735966

Linear OA(25656, 66313, F256, 20) (dual of [66313, 66257, 21]-code), using (u, u+v)-construction based on
  1. linear OA(25617, 775, F256, 10) (dual of [775, 758, 11]-code), using
    • construction XX applied to C1 = C([253,261]), C2 = C([252,260]), C3 = C1 + C2 = C([253,260]), and C∩ = C1 ∩ C2 = C([252,261]) [i] based on
      1. linear OA(25615, 771, F256, 9) (dual of [771, 756, 10]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {253,254,…,261}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(25615, 771, F256, 9) (dual of [771, 756, 10]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {252,253,…,260}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(25617, 771, F256, 10) (dual of [771, 754, 11]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {252,253,…,261}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      4. linear OA(25613, 771, F256, 8) (dual of [771, 758, 9]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {253,254,…,260}, and designed minimum distance d ≥ |I|+1 = 9 [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(25639, 65538, F256, 20) (dual of [65538, 65499, 21]-code), using
    • construction X applied to Ce(19) ⊂ Ce(18) [i] based on
      1. linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
      2. linear OA(25637, 65536, F256, 19) (dual of [65536, 65499, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(25656, 33156, F256, 2, 20) (dual of [(33156, 2), 66256, 21]-NRT-code) [i]OOA Folding
2Linear OOA(25656, 22104, F256, 3, 20) (dual of [(22104, 3), 66256, 21]-NRT-code) [i]
3Linear OOA(25656, 13262, F256, 5, 20) (dual of [(13262, 5), 66254, 21]-NRT-code) [i]