Information on Result #711881

Linear OA(5100, 633, F5, 32) (dual of [633, 533, 33]-code), using construction XX applied to C1 = C([126,156]), C2 = C([128,157]), C3 = C1 + C2 = C([128,156]), and C∩ = C1 ∩ C2 = C([126,157]) based on
  1. linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,156}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  2. linear OA(595, 624, F5, 30) (dual of [624, 529, 31]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,157}, and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {126,127,…,157}, and designed minimum distance d ≥ |I|+1 = 33 [i]
  4. linear OA(591, 624, F5, 29) (dual of [624, 533, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,156}, and designed minimum distance d ≥ |I|+1 = 30 [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(5100, 591, F5, 2, 32) (dual of [(591, 2), 1082, 33]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(5100, 591, F5, 3, 32) (dual of [(591, 3), 1673, 33]-NRT-code) [i]
3Digital (68, 100, 591)-net over F5 [i]
4Linear OA(5101, 637, F5, 32) (dual of [637, 536, 33]-code) [i]VarÅ¡amov–Edel Lengthening
5Linear OOA(5100, 316, F5, 2, 32) (dual of [(316, 2), 532, 33]-NRT-code) [i]OOA Folding
6Linear OOA(5100, 211, F5, 3, 32) (dual of [(211, 3), 533, 33]-NRT-code) [i]