Information on Result #735994

Linear OA(25650, 66313, F256, 18) (dual of [66313, 66263, 19]-code), using (u, u+v)-construction based on
  1. linear OA(25615, 775, F256, 9) (dual of [775, 760, 10]-code), using
    • construction XX applied to C1 = C([254,261]), C2 = C([253,260]), C3 = C1 + C2 = C([254,260]), and C∩ = C1 ∩ C2 = C([253,261]) [i] based on
      1. 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 = {254,255,…,261}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. 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]
      3. 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]
      4. linear OA(25611, 771, F256, 7) (dual of [771, 760, 8]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {254,255,…,260}, and designed minimum distance d ≥ |I|+1 = 8 [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(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
    • construction X applied to Ce(17) ⊂ Ce(16) [i] based on
      1. linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(25650, 33156, F256, 2, 18) (dual of [(33156, 2), 66262, 19]-NRT-code) [i]OOA Folding
2Linear OOA(25650, 22104, F256, 3, 18) (dual of [(22104, 3), 66262, 19]-NRT-code) [i]
3Linear OOA(25650, 13262, F256, 5, 18) (dual of [(13262, 5), 66260, 19]-NRT-code) [i]