Information on Result #732600

Linear OA(2593, 15732, F25, 25) (dual of [15732, 15639, 26]-code), using (u, u+v)-construction based on
  1. linear OA(2521, 108, F25, 12) (dual of [108, 87, 13]-code), using
    • construction XX applied to C1 = C([8,18]), C2 = C([7,17]), C3 = C1 + C2 = C([8,17]), and C∩ = C1 ∩ C2 = C([7,18]) [i] based on
      1. linear OA(2519, 104, F25, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 252−1, defining interval I = {8,9,…,18}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(2519, 104, F25, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 252−1, defining interval I = {7,8,…,17}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      3. linear OA(2521, 104, F25, 12) (dual of [104, 83, 13]-code), using the BCH-code C(I) with length 104 | 252−1, defining interval I = {7,8,…,18}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      4. linear OA(2517, 104, F25, 10) (dual of [104, 87, 11]-code), using the BCH-code C(I) with length 104 | 252−1, defining interval I = {8,9,…,17}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      5. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(2572, 15624, F25, 25) (dual of [15624, 15552, 26]-code), using
    • 1 times truncation [i] based on linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using
      • an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]

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(2593, 7866, F25, 2, 25) (dual of [(7866, 2), 15639, 26]-NRT-code) [i]OOA Folding