Information on Result #732617

Linear OA(2568, 736, F25, 24) (dual of [736, 668, 25]-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(2547, 628, F25, 24) (dual of [628, 581, 25]-code), using
    • construction XX applied to C1 = C([623,21]), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C([623,22]) [i] based on
      1. linear OA(2545, 624, F25, 23) (dual of [624, 579, 24]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
      2. linear OA(2545, 624, F25, 23) (dual of [624, 579, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
      3. linear OA(2547, 624, F25, 24) (dual of [624, 577, 25]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
      4. linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
      5. linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
      6. linear OA(250, 2, F25, 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(2568, 368, F25, 2, 24) (dual of [(368, 2), 668, 25]-NRT-code) [i]OOA Folding