Information on Result #732952

Linear OA(2540, 16256, F25, 11) (dual of [16256, 16216, 12]-code), using (u, u+v)-construction based on
  1. linear OA(259, 628, F25, 5) (dual of [628, 619, 6]-code), using
    • construction XX applied to C1 = C([623,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([623,3]) [i] based on
      1. linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
      2. linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
      4. linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [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(2531, 15628, F25, 11) (dual of [15628, 15597, 12]-code), using
    • construction X applied to Ce(10) ⊂ Ce(9) [i] based on
      1. linear OA(2531, 15625, F25, 11) (dual of [15625, 15594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(2528, 15625, F25, 10) (dual of [15625, 15597, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(2540, 8128, F25, 2, 11) (dual of [(8128, 2), 16216, 12]-NRT-code) [i]OOA Folding
2Linear OOA(2540, 3251, F25, 11, 11) (dual of [(3251, 11), 35721, 12]-NRT-code) [i]OOA Folding and Stacking with Additional Row