Information on Result #712321

Linear OA(5135, 656, F5, 41) (dual of [656, 521, 42]-code), using construction XX applied to C1 = C([125,161]), C2 = C([121,157]), C3 = C1 + C2 = C([125,157]), and C∩ = C1 ∩ C2 = C([121,161]) based on
  1. linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {125,126,…,161}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,157}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  3. linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,161}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {125,126,…,157}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  5. linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
  6. linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)) (see above)

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 OA(5136, 657, F5, 41) (dual of [657, 521, 42]-code) [i]Code Embedding in Larger Space
2Linear OOA(5135, 328, F5, 2, 41) (dual of [(328, 2), 521, 42]-NRT-code) [i]OOA Folding
3Linear OOA(5135, 218, F5, 3, 41) (dual of [(218, 3), 519, 42]-NRT-code) [i]