Information on Result #711344

Linear OA(570, 633, F5, 22) (dual of [633, 563, 23]-code), using construction XX applied to C1 = C([136,156]), C2 = C([138,157]), C3 = C1 + C2 = C([138,156]), and C∩ = C1 ∩ C2 = C([136,157]) based on
  1. linear OA(565, 624, F5, 21) (dual of [624, 559, 22]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,156}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(565, 624, F5, 20) (dual of [624, 559, 21]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {138,139,…,157}, and designed minimum distance d ≥ |I|+1 = 21 [i]
  3. linear OA(569, 624, F5, 22) (dual of [624, 555, 23]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {136,137,…,157}, and designed minimum distance d ≥ |I|+1 = 23 [i]
  4. linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {138,139,…,156}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  5. linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
  6. linear OA(50, 4, F5, 0) (dual of [4, 4, 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(570, 522, F5, 2, 22) (dual of [(522, 2), 974, 23]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(570, 522, F5, 3, 22) (dual of [(522, 3), 1496, 23]-NRT-code) [i]
3Digital (48, 70, 522)-net over F5 [i]
4Linear OOA(570, 316, F5, 2, 22) (dual of [(316, 2), 562, 23]-NRT-code) [i]OOA Folding
5Linear OOA(570, 211, F5, 3, 22) (dual of [(211, 3), 563, 23]-NRT-code) [i]