Information on Result #732866

Linear OA(2556, 16256, F25, 15) (dual of [16256, 16200, 16]-code), using (u, u+v)-construction based on
  1. linear OA(2513, 628, F25, 7) (dual of [628, 615, 8]-code), using
    • construction XX applied to C1 = C([623,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([623,5]) [i] based on
      1. linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      3. linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
      4. linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(2543, 15628, F25, 15) (dual of [15628, 15585, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(13) [i] based on
      1. linear OA(2543, 15625, F25, 15) (dual of [15625, 15582, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
      3. linear OA(250, 3, F25, 0) (dual of [3, 3, 1]-code), using

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(2556, 8128, F25, 2, 15) (dual of [(8128, 2), 16200, 16]-NRT-code) [i]OOA Folding
2Linear OOA(2556, 2322, F25, 15, 15) (dual of [(2322, 15), 34774, 16]-NRT-code) [i]OOA Folding and Stacking with Additional Row