Information on Result #896222

Linear OOA(5150, 4194623, F5, 2, 16) (dual of [(4194623, 2), 8389096, 17]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(529, 322, F5, 2, 8) (dual of [(322, 2), 615, 9]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(529, 644, F5, 8) (dual of [644, 615, 9]-code), using
      • construction XX applied to C1 = C([150,156]), C2 = C([154,157]), C3 = C1 + C2 = C([154,156]), and C∩ = C1 ∩ C2 = C([150,157]) [i] based on
        1. linear OA(521, 624, F5, 7) (dual of [624, 603, 8]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {150,151,…,156}, and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(513, 624, F5, 4) (dual of [624, 611, 5]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {154,155,156,157}, and designed minimum distance d ≥ |I|+1 = 5 [i]
        3. linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {150,151,…,157}, and designed minimum distance d ≥ |I|+1 = 9 [i]
        4. linear OA(59, 624, F5, 3) (dual of [624, 615, 4]-code or 624-cap in PG(8,5)), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {154,155,156}, and designed minimum distance d ≥ |I|+1 = 4 [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(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
  2. linear OOA(5121, 4194301, F5, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(5150, 1048655, F5, 18, 16) (dual of [(1048655, 18), 18875640, 17]-NRT-code) [i]OOA Folding and Stacking with Additional Row