Information on Result #723071

Linear OA(2512, 631, F25, 6) (dual of [631, 619, 7]-code), using construction XX applied to C1 = C([622,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([622,3]) based on
  1. 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 = {−2,−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 6 [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(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 = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [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(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
  6. linear OA(250, 2, F25, 0) (dual of [2, 2, 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(2512, 631, F25, 2, 6) (dual of [(631, 2), 1250, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (6, 12, 631)-net over F25 [i]
3Linear OA(2513, 657, F25, 6) (dual of [657, 644, 7]-code) [i]VarÅ¡amov–Edel Lengthening
4Linear OA(2514, 923, F25, 6) (dual of [923, 909, 7]-code) [i]