Information on Result #710927

Linear OA(538, 633, F5, 12) (dual of [633, 595, 13]-code), using construction XX applied to C1 = C([146,156]), C2 = C([148,157]), C3 = C1 + C2 = C([148,156]), and C∩ = C1 ∩ C2 = C([146,157]) based on
  1. linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,156}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(533, 624, F5, 10) (dual of [624, 591, 11]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {148,149,…,157}, and designed minimum distance d ≥ |I|+1 = 11 [i]
  3. linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,157}, and designed minimum distance d ≥ |I|+1 = 13 [i]
  4. linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {148,149,…,156}, and designed minimum distance d ≥ |I|+1 = 10 [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(538, 430, F5, 2, 12) (dual of [(430, 2), 822, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(538, 430, F5, 3, 12) (dual of [(430, 3), 1252, 13]-NRT-code) [i]
3Digital (26, 38, 430)-net over F5 [i]
4Linear OOA(538, 316, F5, 2, 12) (dual of [(316, 2), 594, 13]-NRT-code) [i]OOA Folding
5Linear OOA(538, 211, F5, 3, 12) (dual of [(211, 3), 595, 13]-NRT-code) [i]